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

The extreme f(x)=-x^4+4x^3 is Saddle(0,0),Maximum(3,27)

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extreme f(x)=-x^4+4x^3

extreme points

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

Saddle (0, 0), Maximum (3, 27)

Solution steps

f^{'} (x) = - 4 x^{3} + 12 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- x^{4} + 4 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

- x^{4} + 4 x^{3} : 27

Maximum (3, 27)

Saddle (0, 0), Maximum (3, 27)

\frac{1}{3} x^{3} - x^{2} + x - 5

f (x) = \frac{x ^{3}}{x ^{3} + 1}

f (x) = 98 y^{2} + x^{2} - x^{2} y

f (x) = \frac{( x + 4 ) ( x - 3 ) ^{2}}{x ^{4} ( x - 1 )}

f (x) = x y - 2 x - 2 y - x^{2} - y^{2}

What is the extreme f(x)=-x^4+4x^3 ?
The extreme f(x)=-x^4+4x^3 is Saddle(0,0),Maximum(3,27)