What is the extreme f(x)=x^4-30x^2+189 ?

The extreme f(x)=x^4-30x^2+189 is Minimum(-sqrt(15),-36),Maximum(0,189),Minimum(sqrt(15),-36)

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extreme f(x)=x^4-30x^2+189

extreme

Minimum (- 15, - 36), Maximum (0, 189), Minimum (15, - 36)

Solution steps

f^{'} (x) = 4 x^{3} - 60 x

Find intervals:

Decreasing

: - \infty < x < - 15,

Increasing

: - 15 < x < 0,

Decreasing

: 0 < x < 15,

Increasing

: 15 < x < \infty

Plug

x = - 15

into

x^{4} - 30 x^{2} + 189 : - 36

Minimum (- 15, - 36)

Plug

x = 0

into

x^{4} - 30 x^{2} + 189 : 189

Maximum (0, 189)

Plug

x = 15

into

x^{4} - 30 x^{2} + 189 : - 36

Minimum (15, - 36)

Minimum (- 15, - 36), Maximum (0, 189), Minimum (15, - 36)

What is the extreme f(x)=x^4-30x^2+189 ?
The extreme f(x)=x^4-30x^2+189 is Minimum(-sqrt(15),-36),Maximum(0,189),Minimum(sqrt(15),-36)