What is the extreme f(x)=24x^3-3x^4 ?

The extreme f(x)=24x^3-3x^4 is Saddle(0,0),Maximum(6,1296)

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extreme f(x)=24x^3-3x^4

extreme points

f (x) = 24 x^{3} - 3 x^{4}

Saddle (0, 0), Maximum (6, 1296)

Solution steps

f^{'} (x) = 72 x^{2} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 6

into

24 x^{3} - 3 x^{4} : 1296

Maximum (6, 1296)

Saddle (0, 0), Maximum (6, 1296)

3 x^{2} - 12 x y + y^{3} + 3 y^{2}

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

1 + \frac{7}{x} - \frac{3}{x ^{2}}

f (x) = \frac{x}{x ^{2} + 1}, - 2 \leq x \leq 2

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

What is the extreme f(x)=24x^3-3x^4 ?
The extreme f(x)=24x^3-3x^4 is Saddle(0,0),Maximum(6,1296)