What is the extreme f(x)=12x^3-24x^2+12x ?

The extreme f(x)=12x^3-24x^2+12x is Maximum(1/3 , 16/9),Minimum(1,0)

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extreme f(x)=12x^3-24x^2+12x

extreme points

f (x) = 12 x^{3} - 24 x^{2} + 12 x

Maximum (\frac{1}{3}, \frac{16}{9}), Minimum (1, 0)

Solution steps

f^{'} (x) = 36 x^{2} - 48 x + 12

Find intervals:

Increasing

: - \infty < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{3}

into

12 x^{3} - 24 x^{2} + 12 x : \frac{16}{9}

Maximum (\frac{1}{3}, \frac{16}{9})

Plug

x = 1

into

12 x^{3} - 24 x^{2} + 12 x : 0

Minimum (1, 0)

Maximum (\frac{1}{3}, \frac{16}{9}), Minimum (1, 0)

f (x, y) = cos^{2} (t) \cdot sin^{2} (t)

f (x) = 7 x - 4 x ln (x)

f (x) = 2 x o n [1.64]

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

What is the extreme f(x)=12x^3-24x^2+12x ?
The extreme f(x)=12x^3-24x^2+12x is Maximum(1/3 , 16/9),Minimum(1,0)