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For the function
f(x)=x^(2)-4, find the slope of the tangent line at
x=-4.
Answer:

For the function $f(x)=x^{2}-4$ , find the slope of the tangent line at $x=-4$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-4

, find the slope of the tangent line at

x=-4

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line at a specific point on the graph of a function, we need to calculate the derivative of the function. The derivative of a function at a point gives us the slope of the tangent line at that point. $\newline$ For the function $f(x) = x^2 - 4$ , we will find the derivative $f'(x)$ . $\newline$ $f'(x) = \frac{d}{dx} (x^2 - 4)$ $\newline$ $f'(x) = 2x$
Find Derivative of $f(x)$ : Now that we have the derivative, we can find the slope of the tangent line at $x = -4$ by plugging $x = -4$ into the derivative. $\newline$ $f'(-4) = 2(-4)$ $\newline$ $f'(-4) = -8$
Find Slope at $x = -4$ : The slope of the tangent line at $x = -4$ is $-8$ . This is the final answer.

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