Chapter 14.4, Problem 35AYU

To determine

To find: The derivative of $f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$ at 8.

Answer to Problem 35AYU

Solution:

$f^{\prime }\left(8\right)=-0.8587$

Explanation of Solution

Given:

$f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$

$c=8$

Formula Used:

The derivative of $y=f\left(x\right)$ at $c$ is given by:

$f^{\prime }\left(c\right)=\underset{x\to c}{\lim }\frac{f\left(x\right)-f\left(c\right)}{x-c}$

Calculation:

Here, $f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$.

Therefore, using the graphing utility calculator we find that,

$f^{\prime }\left(8\right)=-0.8587$