Question

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.
$f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$at$8$

Short answer

Derivative of $f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$at $8$is$f\text{'}\left(8\right)\approx -0.8588$

Step-by-step solution

Step 1. Given information

Given function is

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

and$x=8$

Step 2. Derivative

Enter the function $f\left(x\right)=\frac{-x^3+1}{x^2+5x+7}$and limit $x=8$in the derivative function of the graphing calculator

The graphing calculator shows that the derivative of the function is$f\text{'}\left(8\right)\approx -0.8588$