Question

question 9 (5 points)

find the absolute maximum and absolute minimum values of
\\f(x) = x^3 - 3x^2 - 1\\
on the interval \\(0, 3\\).

please enter:
absolute maximum value is occurs at \\(x =\\)
absolute minimum value is occurs at \\(x =\\)

Explanation:

Find the derivative of the function

Using the Derivative of Polynomials knowledge point

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

Find the critical points in the interval

Using the Critical Points knowledge point

$$
LATEXBLOCK0
$$

Evaluate the function at critical points and endpoints

Using the Absolute Extrema on Closed Intervals knowledge point

$$
LATEXBLOCK1
$$

Identify the absolute maximum and minimum values

Using the Absolute Extrema on Closed Intervals knowledge point

$$
LATEXBLOCK2
$$

Answer:

Find the absolute maximum and absolute minimum values of \(f(x) = x^3 - 3x^2 - 1\) on the interval \([0, 3]\).

Please enter:
Absolute maximum value is <blank>-1</blank>
at x = <blank>0, 3</blank>
Absolute minimum value is <blank>-5</blank>
at x = <blank>2</blank>