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

The extreme f(x)=x^2(1-x)^2 is Minimum(0,0),Maximum(1/2 , 1/16),Minimum(1,0)

Popular >

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

extreme points

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

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{16}), Minimum (1, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

x^{2} (1 - x)^{2} : 0

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

x^{2} (1 - x)^{2} : \frac{1}{16}

Maximum (\frac{1}{2}, \frac{1}{16})

Plug

x = 1

into

x^{2} (1 - x)^{2} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{16}), Minimum (1, 0)

f (x) = 16 + 4 x - x^{2}

f (x) = x e^{- x}, 0 \leq x \leq 2

y = ∣ x + 4 ∣ + \frac{4}{∣ x ∣ - 3}

6 e^{x - 4}

f (x) = \frac{9 x}{x ^{2} + 6}

What is the extreme f(x)=x^2(1-x)^2 ?
The extreme f(x)=x^2(1-x)^2 is Minimum(0,0),Maximum(1/2 , 1/16),Minimum(1,0)