What is the extreme f(x)= 1/4 x^4-2x^2 ?

The extreme f(x)= 1/4 x^4-2x^2 is Minimum(-2,-4),Maximum(0,0),Minimum(2,-4)

Popular >

extreme f(x)= 1/4 x^4-2x^2

extreme points

f (x) = \frac{1}{4} x^{4} - 2 x^{2}

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

\frac{1}{4} x^{4} - 2 x^{2} : - 4

Minimum (- 2, - 4)

Plug

x = 0

into

\frac{1}{4} x^{4} - 2 x^{2} : 0

Maximum (0, 0)

Plug

x = 2

into

\frac{1}{4} x^{4} - 2 x^{2} : - 4

Minimum (2, - 4)

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

f (x) = x^{3} (x - 5)^{2}

f (x) = 1 + 3 x^{2} - 2 x^{3}

f (x) = \frac{1}{4} x + 3 + \frac{400}{x}

f (x) = cos (x) - x

f (x, y) = x + y + 1

What is the extreme f(x)= 1/4 x^4-2x^2 ?
The extreme f(x)= 1/4 x^4-2x^2 is Minimum(-2,-4),Maximum(0,0),Minimum(2,-4)