Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
g(x)=x^(3)-12 x+7.
The absolute maximum value of
g over the closed interval
[-4,5] occurs at what
x-value?
Choose 1 answer:
(A) 5
(B) -2
(C) 2
(D) -4

Let $g(x)=x^{3}-12 x+7$ . $\newline$ The absolute maximum value of $g$ over the closed interval $[-4,5]$ occurs at what $x$ -value? $\newline$ Choose $1$ answer: $\newline$ (A) $5$ $\newline$ (B) $-2$ $\newline$ (C) $2$ $\newline$ (D) $-4$

View step-by-step help

View step-by-step help

Full solution

Q. Let

g(x)=x^{3}-12 x+7

.

\newline

The absolute maximum value of

g

over the closed interval

[-4,5]

occurs at what

x

-value?

\newline

Choose

1

answer:

\newline

(A)

5

\newline

(B)

-2

\newline

(C)

2

\newline

(D)

-4

Calculate Derivative: To find the absolute maximum value of the function $g(x) = x^3 - 12x + 7$ on the closed interval $[-4, 5]$ , we first need to find the critical points of $g(x)$ within the interval. Critical points occur where the derivative $g'(x)$ is zero or undefined. $\newline$ Let's calculate the derivative $g'(x)$ . $\newline$ $g'(x) = \frac{d}{dx} (x^3 - 12x + 7) = 3x^2 - 12.$
Find Critical Points: Now we set the derivative equal to zero to find the critical points. $\newline$ $0 = 3x^2 - 12$ $\newline$ $x^2 = 4$ $\newline$ $x = \pm2$ $\newline$ Both $x = 2$ and $x = -2$ are within the interval $[-4, 5]$ .
Evaluate Function: Next, we evaluate the function $g(x)$ at the critical points and at the endpoints of the interval to determine the absolute maximum. $g(-4) = (-4)^3 - 12(-4) + 7 = -64 + 48 + 7 = -9$ $g(-2) = (-2)^3 - 12(-2) + 7 = -8 + 24 + 7 = 23$ $g(2) = (2)^3 - 12(2) + 7 = 8 - 24 + 7 = -9$ $g(5) = (5)^3 - 12(5) + 7 = 125 - 60 + 7 = 72$
Determine Absolute Maximum: Comparing the values of $g(x)$ at the critical points and endpoints, we find that the absolute maximum value occurs at $x = 5$ , which is $72$ .

More problems from Euler's method

Question

f(x)=x^{3}+6 x^{2}+6 x

c

be the number that satisfies the Mean Value Theorem for

f

on the interval

[-6,0]

\newline

c

\newline

1

\newline

-5

\newline

-4

\newline

-3

\newline

-1

Posted 9 months ago

Question

f(x)=x^{3}+9 x^{2}+13 x

c

be the number that satisfies the Mean Value Theorem for

f

on the interval

-7 \leq x \leq-1

\newline

c

\newline

1

\newline

-6

\newline

-5

\newline

-3

\newline

-2

Posted 9 months ago

Question

h(x)=x^{3}-9 x^{2}+7 x

c

be the number that satisfies the Mean Value Theorem for

h

on the interval

-3 \leq x \leq 6

\newline

c

\newline

1

\newline

-1

\newline

0

\newline

3

\newline

4

Posted 9 months ago

Question

The average cost per meal served at Kiran's restaurant decreases at a rate of

\frac{2400}{q^{2}}

dollars per meal served that month (where

q

is the number of meals served).

\newline

By how many dollars does the average cost per meal decrease between

q=300

q=360

\newline

1

\newline

0

67

\newline

0

81

\newline

1

11

\newline

1

33

Posted 9 months ago

Question

h(x)=-2 x^{3}-7

\newline

The absolute maximum value of

h

over the closed interval

[-3,2]

x

\newline

1

\newline

1

\newline

-2

\newline

2

\newline

-3

Posted 9 months ago

Question

h(x)=x^{3}+6 x^{2}+2

\newline

What is the absolute minimum value of

h

over the closed interval

-6 \leq x \leq 2

\newline

1

\newline

34

\newline

2

\newline

-34

\newline

-2

Posted 9 months ago

Question

g(x)=-2 x^{3}+3 x^{2}+36 x

\newline

The absolute maximum value of

g

over the closed interval

[-3,5]

x

\newline

1

\newline

5

\newline

2

\newline

3

\newline

-3

Posted 9 months ago

Question

h(x)=x^{3}-6 x^{2}+8

\newline

The absolute minimum value of

h

over the closed interval

-1 \leq x \leq 6

x

\newline

1

\newline

-1

\newline

6

\newline

4

\newline

0

Posted 9 months ago

Question

h(x)=-2 x^{3}-7

\newline

The absolute maximum value of

h

over the closed interval

[-3,2]

x

\newline

1

\newline

-3

\newline

2

\newline

1

\newline

-2

Posted 9 months ago

Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 1 month ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant