Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x3 + 3x2 − 72x

Answer 1

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

$f'(x)=3x^2 +6x-72$

Now, we are going to make the derivative equal zero and find the answers of the equation.

$3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0$

So we have that the critical points are the answers to this equation:

$x+6= 0 \\x= - 6$

and

$x-4=0\\x=4$

Thus, the critical points are x=-6 and x=4