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For the function
f(x)=x^(2)-4, find the slope of the tangent line at
x=3.
Answer:

For the function $f(x)=x^{2}-4$ , find the slope of the tangent line at $x=3$ . $\newline$ 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=3

.

\newline

Answer:

Calculate Derivative of Function: To find the slope of the tangent line at a specific point on 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 at Specific Point: Now that we have the derivative, we can find the slope of the tangent line at $x = 3$ by evaluating the derivative at that point. $f'(3) = 2(3)$ $f'(3) = 6$
Evaluate Slope at $x = 3$ : We have found the slope of the tangent line at $x = 3$ to be $6$ . This is the final step in solving the problem.

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