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

The extreme f(x)=3x^4-8x^3 is Saddle(0,0),Minimum(2,-16)

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

extreme points

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

Saddle (0, 0), Minimum (2, - 16)

Solution steps

f^{'} (x) = 12 x^{3} - 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

3 x^{4} - 8 x^{3} : 0

Saddle (0, 0)

Plug

x = 2

into

3 x^{4} - 8 x^{3} : - 16

Minimum (2, - 16)

Saddle (0, 0), Minimum (2, - 16)

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

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

f (x, y) = 2 x^{2} + 3 x y + y^{2} + a x + 5

f (x) = 6 x

f (x) = 4 x ln (x)

What is the extreme f(x)=3x^4-8x^3 ?
The extreme f(x)=3x^4-8x^3 is Saddle(0,0),Minimum(2,-16)