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For the function
f(x)=x^(2)-10, find the slope of the tangent line at
x=7.
Answer:

For the function $f(x)=x^{2}-10$ , find the slope of the tangent line at $x=7$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-10

, find the slope of the tangent line at

x=7

.

\newline

Answer:

Identify Function and Point: Identify the function and the point at which we need to find the slope of the tangent line. $\newline$ We are given the function $f(x) = x^2 - 10$ and we need to find the slope of the tangent line at $x = 7$ .
Recall Tangent Line Slope: Recall that the slope of the tangent line to a function at a given point is the derivative of the function evaluated at that point. $\newline$ To find the slope of the tangent line at $x = 7$ , we need to find the derivative of $f(x)$ with respect to $x$ and then evaluate it at $x = 7$ .
Calculate Derivative: Calculate the derivative of $f(x) = x^2 - 10$ with respect to $x$ . The derivative of $x^2$ with respect to $x$ is $2x$ , and the derivative of a constant is $0$ . Therefore, the derivative of $f(x)$ is $f'(x) = 2x$ .
Evaluate at $x = 7$ : Evaluate the derivative at $x = 7$ to find the slope of the tangent line at that point. $\newline$ $f'(7) = 2 \times 7 = 14$
Conclude Slope is $14$ : Conclude that the slope of the tangent line to the function $f(x)$ at $x = 7$ is $14$ .

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