Question

find all critical values for the function f(x)=8x^3 - 24x + 4, and then list them (separated by commas) in the box below. list of critical numbers:

Explanation:

Step1: Find the derivative

The derivative of $f(x)=8x^{3}-24x + 4$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=24x^{2}-24$.

Step2: Set the derivative equal to zero

Set $f'(x)=0$, so $24x^{2}-24 = 0$. Divide both sides by 24: $x^{2}-1=0$.

Step3: Solve the resulting equation

Factor $x^{2}-1=(x - 1)(x + 1)=0$. Then, by the zero - product property, $x-1 = 0$ or $x + 1=0$. So $x=1$ or $x=-1$.

Answer:

$-1,1$