What is the extreme f(x)=x^4-50x^2+3 ?

The extreme f(x)=x^4-50x^2+3 is Minimum(-5,-622),Maximum(0,3),Minimum(5,-622)

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extreme f(x)=x^4-50x^2+3

extreme

Minimum (- 5, - 622), Maximum (0, 3), Minimum (5, - 622)

Solution steps

f^{'} (x) = 4 x^{3} - 100 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

x^{4} - 50 x^{2} + 3 : - 622

Minimum (- 5, - 622)

Plug

x = 0

into

x^{4} - 50 x^{2} + 3 : 3

Maximum (0, 3)

Plug

x = 5

into

x^{4} - 50 x^{2} + 3 : - 622

Minimum (5, - 622)

Minimum (- 5, - 622), Maximum (0, 3), Minimum (5, - 622)

What is the extreme f(x)=x^4-50x^2+3 ?
The extreme f(x)=x^4-50x^2+3 is Minimum(-5,-622),Maximum(0,3),Minimum(5,-622)