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For the function
f(x)=11x^(2)+12 x+9, find the slope of the tangent line at
x=-9.
Answer:

For the function $f(x)=11 x^{2}+12 x+9$ , find the slope of the tangent line at $x=-9$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=11 x^{2}+12 x+9

, find the slope of the tangent line at

x=-9

.

\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 $x$ .
Evaluate at $x = -9$ : The derivative of $f(x) = 11x^2 + 12x + 9$ with respect to $x$ is $f'(x) = 22x + 12$ .
Substitute $x = -9$ : Now we need to evaluate the derivative at $x = -9$ to find the slope of the tangent line at that point.
Calculate $f'(-9)$ : Substitute $x = -9$ into the derivative to get $f'(-9) = 22(-9) + 12$ .
Simplify Expression: Calculate the value of $f'(-9)$ which is $22(-9) + 12 = -198 + 12$ .
Simplify Expression: Calculate the value of $f'(-9)$ which is $22(-9) + 12 = -198 + 12$ .Simplify the expression to get the final value of the slope at $x = -9$ , which is $-198 + 12 = -186$ .

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