O Find absolute extrema for f(x)= x*-6x² +9x +l in terval [0,5] Gn

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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2) Find absolute extrema for \( f(x) = x^3 - 6x^2 + 9x + 1 \) on interval \([0,5]\).
Transcribed Image Text:2) Find absolute extrema for \( f(x) = x^3 - 6x^2 + 9x + 1 \) on interval \([0,5]\).
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Given that fx=x3-6x2+9x+1To find : absolute extrema on interval  0,5Solution :fx=x3-6x2+9x+1f'x=3x2-12x+9f'x=3x2-4x+3f'x=3x-3x-1f'x=0x-3x-1=0x=3,x=1f0=03-602+90+1 f0=1f1=13-612+91+1f1=5f3=33-632+93+1f3=1f5=53-652+95+1f5=21

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