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For the function
f(x)=x^(2)-8, find the slope of the tangent line at
x=-6.
Answer:

For the function $f(x)=x^{2}-8$ , find the slope of the tangent line at $x=-6$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-8

, find the slope of the tangent line at

x=-6

.

\newline

Answer:

Find Derivative: To find the slope of the tangent line to the function at a specific point, we need to find the derivative of the function, which gives us the slope of the tangent line at any point $x$ . The function is $f(x) = x^2 - 8$ . The derivative of $f(x)$ with respect to $x$ is $f'(x) = 2x$ .
Calculate Derivative: Now we need to evaluate the derivative at $x = -6$ to find the slope of the tangent line at that point. $\newline$ So we substitute $x$ with $-6$ into the derivative. $\newline$ $f'(-6) = 2(-6) = -12$ .
Evaluate at $x = -6$ : The slope of the tangent line at $x = -6$ is therefore $-12$ . $\newline$ This is the final answer.

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