What is the extreme f(x)= 2/(5x^2+1),-2<= x<= 5 ?

The extreme f(x)= 2/(5x^2+1),-2<= x<= 5 is Minimum(-2, 2/21),Maximum(0,2),Minimum(5, 1/63)

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extreme f(x)= 2/(5x^2+1),-2<= x<= 5

extreme points

f (x) = \frac{2}{5 x ^{2} + 1}, - 2 \leq x \leq 5

Minimum (- 2, \frac{2}{21}), Maximum (0, 2), Minimum (5, \frac{1}{63})

Solution steps

Find the critical points:

x = - 2, x = 0, x = 5

Domain of

\frac{2}{5 x ^{2} + 1}, - 2 \leq x \leq 5 : - 2 \leq x \leq 5

Find intervals:

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 5

Plug the extreme point

x = - 2

into

\frac{2}{5 x ^{2} + 1} \Rightarrow y = \frac{2}{21}

Minimum (- 2, \frac{2}{21})

Plug the extreme point

x = 0

into

\frac{2}{5 x ^{2} + 1} \Rightarrow y = 2

Maximum (0, 2)

Plug the extreme point

x = 5

into

\frac{2}{5 x ^{2} + 1} \Rightarrow y = \frac{1}{63}

Minimum (5, \frac{1}{63})

Minimum (- 2, \frac{2}{21}), Maximum (0, 2), Minimum (5, \frac{1}{63})

f (x) = - 1.872 x^{2} + 33.792 - 102.353

f (x) = cos^{(2)} (x) - 2 sin (x)

x^{3} + y^{4} - 9 x - 16 y^{2}

f (x, y) = e^{x y - 2} + (x - 1) y

y = x - 1 - z + 1

What is the extreme f(x)= 2/(5x^2+1),-2<= x<= 5 ?
The extreme f(x)= 2/(5x^2+1),-2<= x<= 5 is Minimum(-2, 2/21),Maximum(0,2),Minimum(5, 1/63)