quiquenobi2v6

2021-12-08

Find the absolute extreme values for $f\left(x\right)={(x+1)}^{2}+3$ on the interval [-2,2].

Carl Swisher

Beginner2021-12-09Added 28 answers

Step 1

To find : the absolute extreme values for$f\left(x\right)={(x+1)}^{2}+3$ on the interval [-2, 2].

Step 2

$f\left(x\right)={(x+1)}^{2}+3$

f′(x)=2(x+1)

To find: the critical values

Put f′(x)=0

$\Rightarrow 2(x+1)=0$

$\Rightarrow 2x+2=0$

$\Rightarrow 2x=-2$

$\Rightarrow x=-1$

Step 3

To check f(x) at the endpoints and at the critical points.

$f(-2)={((-2)+1)}^{2}+3=1+3=4$

$f\left(2\right)={(2+1)}^{2}+3=9+3=12$

$f(-1)={((-1)+1)}^{2}+3=3$

Absolute maximum at x=2 and value=12

Absolute maximum at x=-2 and value=4

To find : the absolute extreme values for

Step 2

f′(x)=2(x+1)

To find: the critical values

Put f′(x)=0

Step 3

To check f(x) at the endpoints and at the critical points.

Absolute maximum at x=2 and value=12

Absolute maximum at x=-2 and value=4

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