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

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

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

extreme points

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

Minimum (1 - 2, 0), Maximum (1, \frac{1}{4}), Minimum (1 + 2, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 1 - 2,

Increasing

: 1 - 2 < x < 1,

Decreasing

: 1 < x < 1 + 2,

Increasing

: 1 + 2 < x < \infty

Plug

x = 1 - 2

into

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

Minimum (1 - 2, 0)

Plug

x = 1

into

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

Maximum (1, \frac{1}{4})

Plug

x = 1 + 2

into

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

Minimum (1 + 2, 0)

Minimum (1 - 2, 0), Maximum (1, \frac{1}{4}), Minimum (1 + 2, 0)

f (x, y) = 2 x^{2} + 3 y^{2} - 4 x - 6

f (x, y) = 400 - 100 x^{2} - 16 y^{2}

f (x, y) = x^{3} + y^{3} + 3 x y^{2} - 18 (x + y)

x, f = \frac{20000}{3 + x ^{2} + y ^{2}}

f (x) = - (x^{2} - 4)

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