What is the extreme f(x)=6x^3-3x^2+6 ?

The extreme f(x)=6x^3-3x^2+6 is Maximum(0,6),Minimum(1/3 , 53/9)

Popular >

extreme f(x)=6x^3-3x^2+6

extreme points

f (x) = 6 x^{3} - 3 x^{2} + 6

Maximum (0, 6), Minimum (\frac{1}{3}, \frac{53}{9})

Solution steps

f^{'} (x) = 18 x^{2} - 6 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

6 x^{3} - 3 x^{2} + 6 : 6

Maximum (0, 6)

Plug

x = \frac{1}{3}

into

6 x^{3} - 3 x^{2} + 6 : \frac{53}{9}

Minimum (\frac{1}{3}, \frac{53}{9})

Maximum (0, 6), Minimum (\frac{1}{3}, \frac{53}{9})

e^{x} (24 - 3 x^{2})

f (x, y) = - 8 x^{2} - 3 y^{2} + 8 x - y + 2

f (x) = - \frac{13}{x ^{2} - 5 x + 35}

f (x) = \frac{3 x ^{2} - 4 x y + 2 y ^{2}}{4 x + 9 y ^{2}}

(x - 2)^{3} + 3

What is the extreme f(x)=6x^3-3x^2+6 ?
The extreme f(x)=6x^3-3x^2+6 is Maximum(0,6),Minimum(1/3 , 53/9)