What is the extreme f(x)=8x^3-x^4=x^3(8-x) ?

The extreme f(x)=8x^3-x^4=x^3(8-x) is Saddle(0,0),Maximum(6,432)

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extreme f(x)=8x^3-x^4=x^3(8-x)

extreme points

f (x) = 8 x^{3} - x^{4} = x^{3} (8 - x)

Saddle (0, 0), Maximum (6, 432)

Solution steps

f^{'} (x) = x^{2} (3 (8 - x) - x)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

x^{3} (8 - x) : 0

Saddle (0, 0)

Plug

x = 6

into

x^{3} (8 - x) : 432

Maximum (6, 432)

Saddle (0, 0), Maximum (6, 432)

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

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

f (x) = x^{3} - \frac{3}{2} x^{2}, - 3 \leq x \leq 6

f (x, y) = e^{2 x} - x^{3} y^{5}

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

What is the extreme f(x)=8x^3-x^4=x^3(8-x) ?
The extreme f(x)=8x^3-x^4=x^3(8-x) is Saddle(0,0),Maximum(6,432)