What is the extreme f(x)=x^4+4x^2-10,-5<= x<= 2 ?

The extreme f(x)=x^4+4x^2-10,-5<= x<= 2 is Maximum(-5,715),Minimum(0,-10),Maximum(2,22)

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extreme f(x)=x^4+4x^2-10,-5<= x<= 2

extreme points

f (x) = x^{4} + 4 x^{2} - 10, - 5 \leq x \leq 2

Maximum (- 5, 715), Minimum (0, - 10), Maximum (2, 22)

Solution steps

Find the critical points:

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

Domain of

x^{4} + 4 x^{2} - 10, - 5 \leq x \leq 2 : - 5 \leq x \leq 2

Find intervals:

Decreasing

: - 5 < x < 0,

Increasing

: 0 < x < 2

Plug the extreme point

x = - 5

into

x^{4} + 4 x^{2} - 10 \Rightarrow y = 715

Maximum (- 5, 715)

Plug the extreme point

x = 0

into

x^{4} + 4 x^{2} - 10 \Rightarrow y = - 10

Minimum (0, - 10)

Plug the extreme point

x = 2

into

x^{4} + 4 x^{2} - 10 \Rightarrow y = 22

Maximum (2, 22)

Maximum (- 5, 715), Minimum (0, - 10), Maximum (2, 22)

What is the extreme f(x)=x^4+4x^2-10,-5<= x<= 2 ?
The extreme f(x)=x^4+4x^2-10,-5<= x<= 2 is Maximum(-5,715),Minimum(0,-10),Maximum(2,22)