Question

Find the derivative of each function at the number indicated using a graphing utility.

$f\left(x\right)=4x^4-3x^3+6x-9at-2$

Short answer

The derivative of the function at the number is about$-158$.

Step-by-step solution

Step 1. Given information.

The given function is,

$f\left(x\right)=4x^4-3x^3+6x-9at-2$

Step 2. Finding the derivative at the given number.

Now we will find the derivative of the given function at the number then we get,

$$\begin{gathered} \frac{df\left(x\right)}{dx}=\frac{d(4x^4-3x^3+6x-9)}{dx} \\ =\frac{d\left(4x^4\right)}{dx}+\frac{d(-3x^3)}{dx}+\frac{d\left(6x\right)}{dx}+\frac{d\left(-9\right)}{dx} \\ =16x^3-9x^2+6 \end{gathered}$$

At $-2$the derivative will be,

$$\begin{gathered} \frac{df\left(x\right)}{dx}=16{\left(-2\right)}^3-9{\left(-2\right)}^2+6 \\ =16\left(-8\right)-9\left(4\right)+6 \\ =-128-36+6 \\ =-158 \end{gathered}$$