Question

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.
$f\left(x\right)=\frac{-5x^4+9x+3}{x^3+5x^2-6}$at$-3$

Short answer

Derivative of$f\left(x\right)=\frac{-5x^4+9x+3}{x^3+5x^2-6}$ at$-3$ is$f\text{'}(-3)=36.8125$

Step-by-step solution

Step 1. Given information

Given function is

$f\left(x\right)=\frac{-5x^4+9x+3}{x^3+5x^2-6}$

and$x=-3$

Step 2. Derivative

Enter the function$f\left(x\right)=\frac{-5x^4+9x+3}{x^3+5x^2-6}$and $x=-3$in the derivative function of the graphing calculator

The graphing calculator shows that the derivative of the function is$f\text{'}(-3)=36.8125$