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For the function
f(x)=12x^(2)-11 x+8, find the slope of the tangent line at
x=-7.
Answer:

For the function $f(x)=12 x^{2}-11 x+8$ , find the slope of the tangent line at $x=-7$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=12 x^{2}-11 x+8

, find the slope of the tangent line at

x=-7

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line to the function at a specific point, we need to calculate the derivative of the function, which gives us the slope of the tangent line at any point $x$ .
Apply Power and Constant Rule: The derivative of $f(x) = 12x^2 - 11x + 8$ with respect to $x$ is $f'(x) = 24x - 11$ . This is found by applying the power rule, which states that the derivative of $x^n$ is $n \cdot x^{(n-1)}$ , and the constant rule, which states that the derivative of a constant is $0$ .
Evaluate Derivative at $x = -7$ : Now we need to evaluate the derivative at $x = -7$ to find the slope of the tangent line at that point. So we substitute $x$ with $-7$ into the derivative: $f'(-7) = 24*(-7) - 11$ .
Calculate Slope: Calculating the value, we get $f'(-7) = -168 - 11 = -179$ .
Final Result: Therefore, the slope of the tangent line to the function at $x = -7$ is $-179$ .

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