What is the extreme f(x)=x^2(7-x)^3 ?

The extreme f(x)=x^2(7-x)^3 is Minimum(0,0),Maximum(14/5 , 1815156/3125),Saddle(7,0)

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extreme f(x)=x^2(7-x)^3

extreme points

f (x) = x^{2} (7 - x)^{3}

Minimum (0, 0), Maximum (\frac{14}{5}, \frac{1815156}{3125}), Saddle (7, 0)

Solution steps

f^{'} (x) = - x (x - 7)^{2} (5 x - 14)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{14}{5},

Decreasing

: \frac{14}{5} < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 0

into

x^{2} (7 - x)^{3} : 0

Minimum (0, 0)

Plug

x = \frac{14}{5}

into

x^{2} (7 - x)^{3} : \frac{1815156}{3125}

Maximum (\frac{14}{5}, \frac{1815156}{3125})

Plug

x = 7

into

x^{2} (7 - x)^{3} : 0

Saddle (7, 0)

Minimum (0, 0), Maximum (\frac{14}{5}, \frac{1815156}{3125}), Saddle (7, 0)

What is the extreme f(x)=x^2(7-x)^3 ?
The extreme f(x)=x^2(7-x)^3 is Minimum(0,0),Maximum(14/5 , 1815156/3125),Saddle(7,0)