What is the extreme x^2(1-x)^3 ?

The extreme x^2(1-x)^3 is Minimum(0,0),Maximum(2/5 , 108/3125),Saddle(1,0)

Popular >

extreme x^2(1-x)^3

extreme points

x^{2} (1 - x)^{3}

Minimum (0, 0), Maximum (\frac{2}{5}, \frac{108}{3125}), Saddle (1, 0)

Solution steps

f^{'} (x) = - x (x - 1)^{2} (5 x - 2)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{2}{5},

Decreasing

: \frac{2}{5} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

x^{2} (1 - x)^{3} : 0

Minimum (0, 0)

Plug

x = \frac{2}{5}

into

x^{2} (1 - x)^{3} : \frac{108}{3125}

Maximum (\frac{2}{5}, \frac{108}{3125})

Plug

x = 1

into

x^{2} (1 - x)^{3} : 0

Saddle (1, 0)

Minimum (0, 0), Maximum (\frac{2}{5}, \frac{108}{3125}), Saddle (1, 0)

4 + x^{3} + y^{3} - 3 x y

p (x) = 3 x^{3} - 13 x^{2} + a x - 8

f (x) = 2 x^{2} - 7 x - 9

f (x) = (x^{2} - 16)^{7}

f (x) = 10 x + 11 x^{\frac{10}{11}}

What is the extreme x^2(1-x)^3 ?
The extreme x^2(1-x)^3 is Minimum(0,0),Maximum(2/5 , 108/3125),Saddle(1,0)