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

The extreme f(x)=x^4+4x^3 is Minimum(-3,-27),Saddle(0,0)

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

extreme points

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

Minimum (- 3, - 27), Saddle (0, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{4} + 4 x^{3} : - 27

Minimum (- 3, - 27)

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- 3, - 27), Saddle (0, 0)

x^{2} + 4 x + 5

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

y = 2 x^{2} - 3 x + 4

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

\frac{5}{x ^{2} - 5 x}

What is the extreme f(x)=x^4+4x^3 ?
The extreme f(x)=x^4+4x^3 is Minimum(-3,-27),Saddle(0,0)