Chapter 14.4, Problem 34AYU

To determine

To find: The derivative of $f\left(x\right)=-5x^4+6x^2-10$ at $5$.

Answer to Problem 34AYU

Solution:

$f^{\prime }\left(5\right)=-2440$

Explanation of Solution

Given:

$f\left(x\right)=-5x^4+6x^2-10$

$c=5$

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, $f\left(x\right)=-5x^4+6x^2-10$.

Therefore, using the graphing utility calculator we find that,

$f^{\prime }\left(5\right)=-2440$