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For the function
f(x)=10x^(2)+7x-6, find the slope of the tangent line at
x=-4.
Answer:

For the function $f(x)=10 x^{2}+7 x-6$ , find the slope of the tangent line at $x=-4$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=10 x^{2}+7 x-6

, find the slope of the tangent line at

x=-4

.

\newline

Answer:

Calculate Derivative: To find the slope of the tangent line 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 $x$ .
Find Derivative Function: The derivative of $f(x) = 10x^2 + 7x - 6$ with respect to $x$ is $f'(x) = 20x + 7$ .
Evaluate at $x = -4$ : Now we need to evaluate the derivative at $x = -4$ to find the slope of the tangent line at that point.
Substitute $x = -4$ : Substitute $x = -4$ into the derivative to get $f'(-4) = 20(-4) + 7$ .
Calculate $f'(-4)$ : Calculate the value of $f'(-4)$ which is $f'(-4) = -80 + 7$ .
Simplify and Final Value: Simplify the expression to get the final value of the slope at $x = -4$ , which is $f'(-4) = -73$ .

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