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For the function
f(x)=x^(2)+2, find the slope of the tangent line at
x=-1.
Answer:

For the function $f(x)=x^{2}+2$ , find the slope of the tangent line at $x=-1$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}+2

, find the slope of the tangent line at

x=-1

.

\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 $f(x) = x^2 + 2$ , we will find the derivative $f'(x)$ .
Find Derivative of $f(x)$ : The derivative of $f(x) = x^2 + 2$ with respect to $x$ is $f'(x) = 2x$ . This is because the derivative of $x^2$ is $2x$ and the derivative of a constant is $0$ .
Evaluate Derivative at $x = -1$ : Now we need to evaluate the derivative at $x = -1$ to find the slope of the tangent line at that point. $\newline$ So we substitute $x = -1$ into the derivative $f'(x) = 2x$ to get $f'(-1) = 2(-1)$ .
Calculate Slope at $x = -1$ : Calculating $f'(-1)$ gives us $2(-1) = -2$ . $\newline$ Therefore, the slope of the tangent line to the function $f(x) = x^2 + 2$ at $x = -1$ is $-2$ .

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