What is the extreme f(x)=x^4+20x^3 ?

The extreme f(x)=x^4+20x^3 is Minimum(-15,-16875),Saddle(0,0)

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extreme f(x)=x^4+20x^3

extreme points

f (x) = x^{4} + 20 x^{3}

Minimum (- 15, - 16875), Saddle (0, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 60 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 15,

Increasing

: - 15 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 15

into

x^{4} + 20 x^{3} : - 16875

Minimum (- 15, - 16875)

Plug

x = 0

into

x^{4} + 20 x^{3} : 0

Saddle (0, 0)

Minimum (- 15, - 16875), Saddle (0, 0)

What is the extreme f(x)=x^4+20x^3 ?
The extreme f(x)=x^4+20x^3 is Minimum(-15,-16875),Saddle(0,0)