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Math Problems
Calculus
Find the slope of a tangent line using limits
Find the
y
y
y
-intercept of the line y = 8 rac{3}{x} - 20.
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
20
x = 20
x
=
20
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
5
x = 5
x
=
5
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
−
5
x = -5
x
=
−
5
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
−
17
x = -17
x
=
−
17
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
17
x = 17
x
=
17
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
11
x = 11
x
=
11
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
k
(
x
)
=
−
1
k(x) = -1
k
(
x
)
=
−
1
at
x
=
11
x = 11
x
=
11
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
13
x = 13
x
=
13
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
−
7
g(x) = -7
g
(
x
)
=
−
7
at
x
=
19
x = 19
x
=
19
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
13
g(x) = 13
g
(
x
)
=
13
at
x
=
9
x = 9
x
=
9
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
k
(
x
)
=
3
k(x) = 3
k
(
x
)
=
3
at
x
=
14
x = 14
x
=
14
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
−
3
x = -3
x
=
−
3
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
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Find the slope of the tangent line to
f
(
x
)
=
−
7
f(x) = -7
f
(
x
)
=
−
7
at
x
=
−
19
x = -19
x
=
−
19
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
−
7
x = -7
x
=
−
7
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
12
x = 12
x
=
12
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
k
(
x
)
=
x
k(x) = x
k
(
x
)
=
x
at
x
=
2
x = 2
x
=
2
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
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Find the slope of the tangent line to
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
at
x
=
−
16
x = -16
x
=
−
16
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
f
(
x
)
=
19
f(x) = 19
f
(
x
)
=
19
at
x
=
2
x = 2
x
=
2
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
19
x = 19
x
=
19
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
Get tutor help
Find the slope of the tangent line to
g
(
x
)
=
x
g(x) = x
g
(
x
)
=
x
at
x
=
8
x = 8
x
=
8
.
\newline
Write your answer as an integer or a fraction. Simplify any fractions.
\newline
____
\newline
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Find the slope of the line tangent to the graph of
f
(
x
)
=
log
3
(
3
−
5
x
2
x
−
5
)
f(x)=\log _{3}\left(\frac{3-5 x}{2 x-5}\right)
f
(
x
)
=
lo
g
3
(
2
x
−
5
3
−
5
x
)
at
x
=
2
x=2
x
=
2
.
\newline
Enter an exact answer.
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2
x
+
4
y
=
15
2
x
+
4
y
=
13
\begin{aligned}2x+4y &= 15 \newline2x+4y &= 13\end{aligned}
2
x
+
4
y
2
x
+
4
y
=
15
=
13
\newline
Consider the given system of equations. How many solutions does this system have?
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Question
\newline
Find the slope of the line tangent to the graph of
f
(
x
)
=
−
3
x
2
−
3
x
+
2
f(x)=-3 x^{2}-3 x+2
f
(
x
)
=
−
3
x
2
−
3
x
+
2
at
x
=
1
x=1
x
=
1
.
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For the function
f
(
x
)
=
6
x
2
+
11
x
+
7
f(x)=6 x^{2}+11 x+7
f
(
x
)
=
6
x
2
+
11
x
+
7
, find the slope of the tangent line at
x
=
8
x=8
x
=
8
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
10
f(x)=x^{2}-10
f
(
x
)
=
x
2
−
10
, find the slope of the tangent line at
x
=
7
x=7
x
=
7
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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For the function
f
(
x
)
=
9
x
2
−
8
x
−
7
f(x)=9 x^{2}-8 x-7
f
(
x
)
=
9
x
2
−
8
x
−
7
, find the slope of the tangent line at
x
=
9
x=9
x
=
9
.
\newline
Answer:
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For the function
f
(
x
)
=
11
x
2
+
12
x
+
9
f(x)=11 x^{2}+12 x+9
f
(
x
)
=
11
x
2
+
12
x
+
9
, find the slope of the tangent line at
x
=
−
9
x=-9
x
=
−
9
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
2
f(x)=x^{2}+2
f
(
x
)
=
x
2
+
2
, find the slope of the tangent line at
x
=
−
1
x=-1
x
=
−
1
.
\newline
Answer:
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For the function
f
(
x
)
=
2
x
−
6
f(x)=2 x-6
f
(
x
)
=
2
x
−
6
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
−
8
x
2
+
9
x
+
9
f(x)=-8 x^{2}+9 x+9
f
(
x
)
=
−
8
x
2
+
9
x
+
9
, find the slope of the tangent line at
x
=
9
x=9
x
=
9
.
\newline
Answer:
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For the function
f
(
x
)
=
3
x
2
+
7
x
+
4
f(x)=3 x^{2}+7 x+4
f
(
x
)
=
3
x
2
+
7
x
+
4
, find the slope of the tangent line at
x
=
6
x=6
x
=
6
.
\newline
Answer:
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For the function
f
(
x
)
=
−
7
x
2
+
3
x
−
5
f(x)=-7 x^{2}+3 x-5
f
(
x
)
=
−
7
x
2
+
3
x
−
5
, find the slope of the tangent line at
x
=
3
x=3
x
=
3
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
8
f(x)=x^{2}-8
f
(
x
)
=
x
2
−
8
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
3
x=3
x
=
3
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
11
f(x)=x^{2}-11
f
(
x
)
=
x
2
−
11
, find the slope of the tangent line at
x
=
12
x=12
x
=
12
.
\newline
Answer:
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For the function
f
(
x
)
=
−
6
x
−
9
f(x)=-6 x-9
f
(
x
)
=
−
6
x
−
9
, find the slope of the tangent line at
x
=
1
x=1
x
=
1
.
\newline
Answer:
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For the function
f
(
x
)
=
−
6
x
2
+
9
x
+
2
f(x)=-6 x^{2}+9 x+2
f
(
x
)
=
−
6
x
2
+
9
x
+
2
, find the slope of the tangent line at
x
=
2
x=2
x
=
2
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the tangent line at
x
=
1
x=1
x
=
1
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
11
f(x)=x^{2}-11
f
(
x
)
=
x
2
−
11
, find the slope of the tangent line at
x
=
−
3
x=-3
x
=
−
3
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
3
f(x)=x^{2}-3
f
(
x
)
=
x
2
−
3
, find the slope of the tangent line at
x
=
12
x=12
x
=
12
.
\newline
Answer:
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For the function
f
(
x
)
=
10
x
2
+
7
x
−
6
f(x)=10 x^{2}+7 x-6
f
(
x
)
=
10
x
2
+
7
x
−
6
, find the slope of the tangent line at
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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For the function
f
(
x
)
=
12
x
2
−
11
x
+
8
f(x)=12 x^{2}-11 x+8
f
(
x
)
=
12
x
2
−
11
x
+
8
, find the slope of the tangent line at
x
=
−
7
x=-7
x
=
−
7
.
\newline
Answer:
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For the function
f
(
x
)
=
10
x
+
3
f(x)=10 x+3
f
(
x
)
=
10
x
+
3
, find the slope of the tangent line at
x
=
11
x=11
x
=
11
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
5
f(x)=x^{2}+5
f
(
x
)
=
x
2
+
5
, find the slope of the tangent line at
x
=
5
x=5
x
=
5
.
\newline
Answer:
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For the function
f
(
x
)
=
−
9
x
−
9
f(x)=-9 x-9
f
(
x
)
=
−
9
x
−
9
, find the slope of the tangent line at
x
=
−
6
x=-6
x
=
−
6
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
+
3
f(x)=x^{2}+3
f
(
x
)
=
x
2
+
3
, find the slope of the secant line between
x
=
2
x=2
x
=
2
and
x
=
4
x=4
x
=
4
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
4
f(x)=x^{2}-4
f
(
x
)
=
x
2
−
4
, find the slope of the secant line between
x
=
−
4
x=-4
x
=
−
4
and
x
=
−
1
x=-1
x
=
−
1
.
\newline
Answer:
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For the function
f
(
x
)
=
x
2
−
7
f(x)=x^{2}-7
f
(
x
)
=
x
2
−
7
, find the slope of the secant line between
x
=
−
6
x=-6
x
=
−
6
and
x
=
−
4
x=-4
x
=
−
4
.
\newline
Answer:
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