Chapter 14.4, Problem 36AYU

To determine

To find: The derivative of $f\left(x\right)=\frac{-5x^4+9x+3}{x^3+5x^2-6}$ at $-3$.

Answer to Problem 36AYU

Solution:

$f^{\prime }\left(-3\right)=36.8125$

Explanation of Solution

Given:

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

$c=-3$

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

Therefore, using the graphing utility calculator we find that,

$f^{\prime }\left(-3\right)=36.8125$