What is the extreme f(x)=4x^3-108x^2+729x ?

The extreme f(x)=4x^3-108x^2+729x is Maximum(9/2 ,1458),Minimum(27/2 ,0)

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extreme f(x)=4x^3-108x^2+729x

extreme points

f (x) = 4 x^{3} - 108 x^{2} + 729 x

Maximum (\frac{9}{2}, 1458), Minimum (\frac{27}{2}, 0)

Solution steps

f^{'} (x) = 12 x^{2} - 216 x + 729

Find intervals:

Increasing

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

Decreasing

: \frac{9}{2} < x < \frac{27}{2},

Increasing

: \frac{27}{2} < x < \infty

Plug

x = \frac{9}{2}

into

4 x^{3} - 108 x^{2} + 729 x : 1458

Maximum (\frac{9}{2}, 1458)

Plug

x = \frac{27}{2}

into

4 x^{3} - 108 x^{2} + 729 x : 0

Minimum (\frac{27}{2}, 0)

Maximum (\frac{9}{2}, 1458), Minimum (\frac{27}{2}, 0)

f (x) = 4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

- x^{3} + 6 x^{2} + 15 x + 4

f (x) = x^{2} - 5 x - 1

f (x) = x x + 8

f (x) = \frac{x + 2}{x ^{2} - 3 x - 10}

What is the extreme f(x)=4x^3-108x^2+729x ?
The extreme f(x)=4x^3-108x^2+729x is Maximum(9/2 ,1458),Minimum(27/2 ,0)