What is the extreme y=3x^3(x-5)^2 ?

The extreme y=3x^3(x-5)^2 is Saddle(0,0),Maximum(3,324),Minimum(5,0)

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extreme y=3x^3(x-5)^2

extreme points

y = 3 x^{3} (x - 5)^{2}

Saddle (0, 0), Maximum (3, 324), Minimum (5, 0)

Solution steps

f^{'} (x) = 3 (5 x^{4} - 40 x^{3} + 75 x^{2})

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

3 x^{3} (x - 5)^{2} : 0

Saddle (0, 0)

Plug

x = 3

into

3 x^{3} (x - 5)^{2} : 324

Maximum (3, 324)

Plug

x = 5

into

3 x^{3} (x - 5)^{2} : 0

Minimum (5, 0)

Saddle (0, 0), Maximum (3, 324), Minimum (5, 0)

y = \frac{1}{x - 8} - 9

y = x + \frac{25}{x}

f (x) = \frac{3 x ^{2}}{x - 2}, - 2 \leq x \leq 1

f (x) = x (16 - 41 + 2 x) (\frac{41}{2} - x)

g (x, y) = 4 - x^{(2)} - y^{(2)}

What is the extreme y=3x^3(x-5)^2 ?
The extreme y=3x^3(x-5)^2 is Saddle(0,0),Maximum(3,324),Minimum(5,0)