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

The extreme f(x)=x^2(2-x)^3 is Minimum(0,0),Maximum(4/5 , 3456/3125),Saddle(2,0)

Popular >

extreme f(x)=x^2(2-x)^3

extreme points

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

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{3456}{3125}), Saddle (2, 0)

Solution steps

f^{'} (x) = - x (x - 2)^{2} (5 x - 4)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{4}{5},

Decreasing

: \frac{4}{5} < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{4}{5}

into

x^{2} (2 - x)^{3} : \frac{3456}{3125}

Maximum (\frac{4}{5}, \frac{3456}{3125})

Plug

x = 2

into

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

Saddle (2, 0)

Minimum (0, 0), Maximum (\frac{4}{5}, \frac{3456}{3125}), Saddle (2, 0)

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

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

9 x^{2} + 18 x + 7

f (x) = \frac{x - 3}{x ^{2}}

f (x) = x^{2} - 10 x - 5

What is the extreme f(x)=x^2(2-x)^3 ?
The extreme f(x)=x^2(2-x)^3 is Minimum(0,0),Maximum(4/5 , 3456/3125),Saddle(2,0)