Find the absolute extreme values for f(x)=(x+1)^{2}+3 on the interval

quiquenobi2v6

quiquenobi2v6

Answered question

2021-12-08

Find the absolute extreme values for f(x)=(x+1)2+3 on the interval [-2,2].

Answer & Explanation

Carl Swisher

Carl Swisher

Beginner2021-12-09Added 28 answers

Step 1
To find : the absolute extreme values for f(x)=(x+1)2+3 on the interval [-2, 2].
Step 2
f(x)=(x+1)2+3
f′(x)=2(x+1)
To find: the critical values
Put f′(x)=0
2(x+1)=0
2x+2=0
2x=2
x=1
Step 3
To check f(x) at the endpoints and at the critical points.
f(2)=((2)+1)2+3=1+3=4
f(2)=(2+1)2+3=9+3=12
f(1)=((1)+1)2+3=3
Absolute maximum at x=2 and value=12
Absolute maximum at x=-2 and value=4

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