# Can you show me the steps to solve the problem?3.1Directions: Find the absolute maximum and absolute minimum values of f on the given interval.47) f(x) = 2x3 - 3x2 - 12x + 1 [-2, 3]

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Can you show me the steps to solve the problem?

3.1

Directions: Find the absolute maximum and absolute minimum values of f on the given interval.

47) f(x) = 2x3 - 3x2 - 12x + 1 [-2, 3]

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Step 1

Given a function and an interval, help_outlineImage Transcriptionclose2x33x212x 1 f(x) = To calculate: The absolute maximum and minimum for the function on interval [-2, 3] fullscreen
Step 2

Note: help_outlineImage TranscriptioncloseFormula used: To find absolute maximum and minimum of a function, 1. Set the first derivative of the function to zero, f' (a)= 0, to find the critical values of the function 2. Substitute the critical values intof (x) 3. Substitute the end points into f (x) The maximum value is absolute maximum and the minimum value is absolute minimum fullscreen
Step 3

Begin with calculating the first derivative of... help_outlineImage Transcriptionclosef' (x) 6x 6x - 12 6x2 - x - 2) Now, set f'(x) 0 6(x2 x 2) = 0 6(x2 2x x- 2) 0 6(x(x 2)1x 2)) 0 6(x 1)(x 2) = 0 Thus, either x +1 0 or x - 2 0. fullscreen

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### Calculus 