What is the extreme f(x)=x^4+2x^2-3,-2<= x<= 2 ?

The extreme f(x)=x^4+2x^2-3,-2<= x<= 2 is Maximum(-2,21),Minimum(0,-3),Maximum(2,21)

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extreme f(x)=x^4+2x^2-3,-2<= x<= 2

extreme points

f (x) = x^{4} + 2 x^{2} - 3, - 2 \leq x \leq 2

Maximum (- 2, 21), Minimum (0, - 3), Maximum (2, 21)

Solution steps

Find the critical points:

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

Domain of

x^{4} + 2 x^{2} - 3, - 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

x^{4} + 2 x^{2} - 3 \Rightarrow y = 21

Maximum (- 2, 21)

Plug the extreme point

x = 0

into

x^{4} + 2 x^{2} - 3 \Rightarrow y = - 3

Minimum (0, - 3)

Plug the extreme point

x = 2

into

x^{4} + 2 x^{2} - 3 \Rightarrow y = 21

Maximum (2, 21)

Maximum (- 2, 21), Minimum (0, - 3), Maximum (2, 21)

P (a, b) = a^{3} - b^{3} + a^{2} + ab + b^{2}

f (x) = 8 x^{3} + 81 x^{2} - 42 x - 8

x^{\frac{5}{3}} - 5 x^{\frac{2}{3}}

f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

f (x) = x + \frac{36}{x}

What is the extreme f(x)=x^4+2x^2-3,-2<= x<= 2 ?
The extreme f(x)=x^4+2x^2-3,-2<= x<= 2 is Maximum(-2,21),Minimum(0,-3),Maximum(2,21)