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

The extreme f(x)=(x^2)/(x^2+1),-2<= x<= 2 is Maximum(-2, 4/5),Minimum(0,0),Maximum(2, 4/5)

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

extreme points

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

Maximum (- 2, \frac{4}{5}), Minimum (0, 0), Maximum (2, \frac{4}{5})

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2

Plug the extreme point

x = - 2

into

\frac{x ^{2}}{x ^{2} + 1} \Rightarrow y = \frac{4}{5}

Maximum (- 2, \frac{4}{5})

Plug the extreme point

x = 0

into

\frac{x ^{2}}{x ^{2} + 1} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 2

into

\frac{x ^{2}}{x ^{2} + 1} \Rightarrow y = \frac{4}{5}

Maximum (2, \frac{4}{5})

Maximum (- 2, \frac{4}{5}), Minimum (0, 0), Maximum (2, \frac{4}{5})

f (x) = x 1 - 5 x

f (x, y) = 9 x^{2} + 3 x y + 9 y^{2} + 7 x y^{2} + 3 x^{2} y

y = - 5 x^{2} - 6 x + 2

f (x) = x^{3} + y^{3} - 6 x y + 27

f (x) = 4 (x^{(\frac{10}{3})}) - 10 (x^{(\frac{4}{3})})

What is the extreme f(x)=(x^2)/(x^2+1),-2<= x<= 2 ?
The extreme f(x)=(x^2)/(x^2+1),-2<= x<= 2 is Maximum(-2, 4/5),Minimum(0,0),Maximum(2, 4/5)