Question

Find the critical numbers of the function f(x) = 12x ^ 5 - 15x ^ 4 - 80x ^ 3 - 7 and classify them using a graph.

Answer 1

Step-by-step explanation

Given the function

`f\left(x\right)=12x^5-15x^4-80x^3-7`

We can find the critical points by plotting the graph of the function below.

From the graph, the critical points are as follows

Answer:

Number 1

`x=-1.5616\Rightarrow local\text{ max}`

Number 2

`x=2.5616\frac{}{}\Rightarrow local\text{ min}`

Number 3

`x=0\Rightarrow neither\text{ }a\text{ max or min}`