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For the function
f(x)=10 x+3, find the slope of the tangent line at
x=11.
Answer:

For the function $f(x)=10 x+3$ , find the slope of the tangent line at $x=11$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=10 x+3

, find the slope of the tangent line at

x=11

.

\newline

Answer:

Identify Function Type: Identify the type of function and the process to find the slope of the tangent line. $\newline$ The function $f(x) = 10x + 3$ is a linear function. The slope of the tangent line to a linear function is the same as the slope of the function itself, because the graph of a linear function is a straight line.
Find Slope Process: Determine the slope of the function. $\newline$ For a linear function in the form $f(x) = mx + b$ , the slope is the coefficient of $x$ , which is $m$ . In this case, the function is $f(x) = 10x + 3$ , so the slope $m$ is $10$ .
Determine Slope: Since the slope of the function is constant, the slope of the tangent line at any point $x$ is the same as the slope of the function. $\newline$ Therefore, the slope of the tangent line at $x = 11$ is also $10$ .

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