What is the extreme f(x)=x^3-27x^2+216x ?

The extreme f(x)=x^3-27x^2+216x is Maximum(6,540),Minimum(12,432)

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extreme f(x)=x^3-27x^2+216x

extreme points

f (x) = x^{3} - 27 x^{2} + 216 x

Maximum (6, 540), Minimum (12, 432)

Solution steps

f^{'} (x) = 3 x^{2} - 54 x + 216

Find intervals:

Increasing

: - \infty < x < 6,

Decreasing

: 6 < x < 12,

Increasing

: 12 < x < \infty

Plug

x = 6

into

x^{3} - 27 x^{2} + 216 x : 540

Maximum (6, 540)

Plug

x = 12

into

x^{3} - 27 x^{2} + 216 x : 432

Minimum (12, 432)

Maximum (6, 540), Minimum (12, 432)

f (x) = (9 x^{2} - 1) (1 + 4 y)

f (x) = 2 x^{3} + 6 x - 9

\frac{1}{3} π r^{2} h

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

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

What is the extreme f(x)=x^3-27x^2+216x ?
The extreme f(x)=x^3-27x^2+216x is Maximum(6,540),Minimum(12,432)