Maximum of a Fourth-Degree Polynomial Find the maxi- mum value of the function f(x) = 3 + 4x – x [Hint: Let t = x².]

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Maximum of a Fourth-Degree Polynomial Find the maxi-
mum value of the function
f(x) = 3 + 4x – x
[Hint: Let t = x².]
Transcribed Image Text:Maximum of a Fourth-Degree Polynomial Find the maxi- mum value of the function f(x) = 3 + 4x – x [Hint: Let t = x².]
Expert Solution
Step 1

The given function f(x) - f(x) = 3+4x2-x4f(x) = 3+4x2-x22         ..............(1)Substituting t = x2f(t) = 3+4t-t2Now, differentiating with respect to t - f'(t) = ddt3+4t-t2f'(t) = 0+4-2tf'(t) = 4-2tTo find the point where, the function is maximum, putting f'(t) = 04-2t = 0-2t = -4t = -4-2t = 2

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