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For the function
f(x)=9x^(2)-8x-7, find the slope of the tangent line at
x=9.
Answer:

For the function $f(x)=9 x^{2}-8 x-7$ , 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)=9 x^{2}-8 x-7

, find the slope of the tangent line at

x=9

.

\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 $x$ .
Evaluate at $x = 9$ : The derivative of $f(x) = 9x^2 - 8x - 7$ with respect to $x$ is $f'(x) = 18x - 8$ .
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 Result: Substitute $x = 9$ into the derivative to get $f'(9) = 18(9) - 8$ .
Calculate Result: Substitute $x = 9$ into the derivative to get $f'(9) = 18(9) - 8$ . Calculate $f'(9) = 162 - 8$ .
Calculate Result: Substitute $x = 9$ into the derivative to get $f'(9) = 18(9) - 8$ .Calculate $f'(9) = 162 - 8$ .The result is $f'(9) = 154$ . This is the slope of the tangent line at $x = 9$ .

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