question 1 (1 point)\nwhat are the minimum and maximum values of the function f(x)=x³ on the interval…

question 1 (1 point)\nwhat are the minimum and maximum values of the function f(x)=x³ on the interval -3,2?\n\na minimum: -27; maximum: 8\nb minimum: -3; maximum: 2\nc minimum: 4; maximum: 9\nd minimum: 8; maximum: 27

question 1 (1 point)\nwhat are the minimum and maximum values of the function f(x)=x³ on the interval -3,2?\n\na minimum: -27; maximum: 8\nb minimum: -3; maximum: 2\nc minimum: 4; maximum: 9\nd minimum: 8; maximum: 27

Answer

Explanation:

Step1: Evaluate function at endpoints

For $x = - 3$, $f(-3)=(-3)^3=-27$. For $x = 2$, $f(2)=2^3 = 8$.

Step2: Check for critical - points

Differentiate $f(x)=x^3$, $f^\prime(x)=3x^2$. Set $f^\prime(x) = 0$, we get $3x^2=0$, so $x = 0$. And $f(0)=0^3 = 0$.

Step3: Compare values

We have $f(-3)=-27$, $f(0)=0$, $f(2)=8$. The minimum value is $-27$ and the maximum value is $8$.

Answer:

A. minimum: $-27$; maximum: $8$