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Derivative Test. (d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c). (e) Indicate any absolute maximum or minimum values that exist for this function f.

Derivative Test. (d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c). (e) Indicate any absolute maximum or minimum values that exist for this function f.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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NEED HELP WITH PART E AND D, PLEASE.

1. Let f(x)= 3x² - 4x³ - 12x². (a) Find all critical numbers for the function f. (b) Determine all those intervals on which the graph of f is increasing and all those on which it is decreasing by analyzing the sign of the derivative function. (c) Find and classify all of the relative extreme values/points by applying the First Derivative Test. (d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c). (e) Indicate any absolute maximum or minimum values that exist for this function f.
Transcribed Image Text:1. Let f(x)= 3x² - 4x³ - 12x². (a) Find all critical numbers for the function f. (b) Determine all those intervals on which the graph of f is increasing and all those on which it is decreasing by analyzing the sign of the derivative function. (c) Find and classify all of the relative extreme values/points by applying the First Derivative Test. (d) Sketch a graph of y = f (x) based on your findings in parts (a) - (c). (e) Indicate any absolute maximum or minimum values that exist for this function f.
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