What is the extreme f(x)=x^4-72x^2+7 ?

The extreme f(x)=x^4-72x^2+7 is Minimum(-6,-1289),Maximum(0,7),Minimum(6,-1289)

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extreme f(x)=x^4-72x^2+7

extreme points

f (x) = x^{4} - 72 x^{2} + 7

Minimum (- 6, - 1289), Maximum (0, 7), Minimum (6, - 1289)

Solution steps

f^{'} (x) = 4 x^{3} - 144 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

x^{4} - 72 x^{2} + 7 : - 1289

Minimum (- 6, - 1289)

Plug

x = 0

into

x^{4} - 72 x^{2} + 7 : 7

Maximum (0, 7)

Plug

x = 6

into

x^{4} - 72 x^{2} + 7 : - 1289

Minimum (6, - 1289)

Minimum (- 6, - 1289), Maximum (0, 7), Minimum (6, - 1289)

f (x, y) = x^{2} + 6 x + y^{3} - 6 y^{2} + 10

f (x) = 4 x + 324 x, 0 < x < \infty

f (x) = 2 x^{4} + 3 x^{3} - 7 x^{2} - 2 x - 24

f (x) = x^{2} - 9, - \frac{9}{2} \leq x \leq 6

x^{2} e^{- 6 x}

What is the extreme f(x)=x^4-72x^2+7 ?
The extreme f(x)=x^4-72x^2+7 is Minimum(-6,-1289),Maximum(0,7),Minimum(6,-1289)