Question

Find the absolute maximum and absolute minimum values of $f(x) = x^3 - 3x^2 - 24x - 8$ on $[-4, 2]$, along with where they occur. The absolute minimum value is , occuring when $x = $ The absolute maximum value is , occuring when $x = $ Enter here (using math notation or by porting in an image) an outline of how you arrived at your solution.

          Find the absolute maximum and absolute minimum values of $f(x) = x^3 - 3x^2 - 24x - 8$ on $[-4, 2]$,
along with where they occur.
The absolute minimum value is 
, occuring when $x = $
The absolute maximum value is 
, occuring when $x = $
Enter here (using math notation or by porting in an image) an outline of how you arrived at your solution.

Find the absolute maximum and absolute minimum values of f(x) = x^3 - 3x^2 - 24x - 8 on [-4, 2],
along with where they occur.
The absolute minimum value is
, occuring when x =
The absolute maximum value is
, occuring when x =
Enter here (using math notation or by porting in an image) an outline of how you arrived at your solution.

Added by Sarah M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

07/29/2023

Step 1

To find the critical points, we need to find where the derivative of f(x) is equal to 0 or undefined. f'(x) = 3x^2 - 6x - 24 Setting f'(x) = 0, we get: 3x^2 - 6x - 24 = 0 Dividing by 3, we get: x^2 - 2x - 8 = 0 Factoring the quadratic equation, we get: (x - 4)(x + Show more…

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Find the absolute maximum and absolute minimum values of f(x) = x^3 - 3x^2 - 24x - 8 on the interval [-4, 2], along with where they occur. The absolute minimum value is -35, occurring when x = -4. The absolute maximum value is -8, occurring when x = 2. Find the absolute maximum and absolute minimum values of f(x) = x^3 - 3x^2 - 24x - 8 on the interval [-4, 2], along with where they occur. The absolute minimum value is -35, occurring when x = -4. The absolute maximum value is -8, occurring when x = 2.