What is the extreme f(x)= 4/3 x^3-12x^2+27x-6 ?

The extreme f(x)= 4/3 x^3-12x^2+27x-6 is Maximum(3/2 ,12),Minimum(9/2 ,-6)

Popular >

extreme f(x)= 4/3 x^3-12x^2+27x-6

extreme points

f (x) = \frac{4}{3} x^{3} - 12 x^{2} + 27 x - 6

Maximum (\frac{3}{2}, 12), Minimum (\frac{9}{2}, - 6)

Solution steps

f^{'} (x) = 4 x^{2} - 24 x + 27

Find intervals:

Increasing

: - \infty < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < \frac{9}{2},

Increasing

: \frac{9}{2} < x < \infty

Plug

x = \frac{3}{2}

into

\frac{4}{3} x^{3} - 12 x^{2} + 27 x - 6 : 12

Maximum (\frac{3}{2}, 12)

Plug

x = \frac{9}{2}

into

\frac{4}{3} x^{3} - 12 x^{2} + 27 x - 6 : - 6

Minimum (\frac{9}{2}, - 6)

Maximum (\frac{3}{2}, 12), Minimum (\frac{9}{2}, - 6)

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

f (x) = x^{5} - 5 x^{4} + 1

f (x) = x^{3} - 9 x^{2} + 15 x + 4

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

f (x, y) = x^{3} + y^{3} - 3 x^{2} - 3 y + 10

What is the extreme f(x)= 4/3 x^3-12x^2+27x-6 ?
The extreme f(x)= 4/3 x^3-12x^2+27x-6 is Maximum(3/2 ,12),Minimum(9/2 ,-6)