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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - 16)

Plug

x = 0

into

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

Saddle (0, 0)

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

\frac{( x - 1 ) ^{3}}{x ^{2}}

f (x) = \frac{2}{x + 3}

f (x) = - \frac{11}{( 5 + x ) ^{2}}

f (x) = \frac{6 + x}{x ^{2} ( 6 - x )}

f (x) = - 3 (x + 2)

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