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

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

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

extreme points

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

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

Solution steps

f^{'} (x) = - 12 x^{2} (x - 6)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

x^{3} (24 - 3 x) : 0

Saddle (0, 0)

Plug

x = 6

into

x^{3} (24 - 3 x) : 1296

Maximum (6, 1296)

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

f (x) = x^{2} + 5 x - 77

f (x) = x^{5} - 5 x^{4} + 5 x^{3} - 10

f (x) = 8 x - 8 ln (x^{2}), (0, + \infty)

f (x, y) = 7 x^{2} y - 8 x y^{3} + 9 y^{3}

\frac{8 - x ^{3}}{x ^{2}}

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