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grigory [225]
3 years ago
8

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
Mathematics
1 answer:
Furkat [3]3 years ago
8 0

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

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