What is the extreme 1/(x^2+2x+2),-2<= x<= 2 ?

The extreme 1/(x^2+2x+2),-2<= x<= 2 is Minimum(-2, 1/2),Maximum(-1,1),Minimum(2, 1/10)

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extreme 1/(x^2+2x+2),-2<= x<= 2

extreme points

\frac{1}{x ^{2} + 2 x + 2}, - 2 \leq x \leq 2

Minimum (- 2, \frac{1}{2}), Maximum (- 1, 1), Minimum (2, \frac{1}{10})

Solution steps

Find the critical points:

x = - 2, x = - 1, x = 2

Domain of

\frac{1}{x ^{2} + 2 x + 2}, - 2 \leq x \leq 2 : - 2 \leq x \leq 2

Find intervals:

Increasing

: - 2 < x < - 1,

Decreasing

: - 1 < x < 2

Plug the extreme point

x = - 2

into

\frac{1}{x ^{2} + 2 x + 2} \Rightarrow y = \frac{1}{2}

Minimum (- 2, \frac{1}{2})

Plug the extreme point

x = - 1

into

\frac{1}{x ^{2} + 2 x + 2} \Rightarrow y = 1

Maximum (- 1, 1)

Plug the extreme point

x = 2

into

\frac{1}{x ^{2} + 2 x + 2} \Rightarrow y = \frac{1}{10}

Minimum (2, \frac{1}{10})

Minimum (- 2, \frac{1}{2}), Maximum (- 1, 1), Minimum (2, \frac{1}{10})

3 x - 10 y = 20

(- 1, 4), (4, - 2)

f (x) = x^{2} + x

y = sin (cos (tan (π x)))

(- 4, 5), (7, 18)

What is the extreme 1/(x^2+2x+2),-2<= x<= 2 ?
The extreme 1/(x^2+2x+2),-2<= x<= 2 is Minimum(-2, 1/2),Maximum(-1,1),Minimum(2, 1/10)