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For the function
f(x)=x^(2)-11, find the slope of the tangent line at
x=12.
Answer:

For the function $f(x)=x^{2}-11$ , find the slope of the tangent line at $x=12$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-11

, find the slope of the tangent line at

x=12

.

\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 at that point. The derivative of a function at a point gives us the slope of the tangent line to the function at that point.
Apply Power Rule: The function given is $f(x) = x^2 - 11$ . To find the derivative of this function, we use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ . So, the derivative of $x^2$ is $2\cdot x^{(2-1)} = 2x$ .
Evaluate Derivative at $x=12$ : Now we need to evaluate the derivative at $x = 12$ to find the slope of the tangent line at that point. We substitute $x$ with $12$ in the derivative we found, which is $2x$ . So, the slope at $x = 12$ is $2\times 12$ .
Calculate Slope at $x=12$ : Calculating the slope at $x = 12$ gives us $2\times 12 = 24$ . Therefore, the slope of the tangent line to the function $f(x) = x^2 - 11$ at $x = 12$ is $24$ .

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