What is the extreme f(x)=4x^4+16x^3 ?

The extreme f(x)=4x^4+16x^3 is Minimum(-3,-108),Saddle(0,0)

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extreme f(x)=4x^4+16x^3

extreme points

f (x) = 4 x^{4} + 16 x^{3}

Minimum (- 3, - 108), Saddle (0, 0)

Solution steps

f^{'} (x) = 16 x^{3} + 48 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

4 x^{4} + 16 x^{3} : - 108

Minimum (- 3, - 108)

Plug

x = 0

into

4 x^{4} + 16 x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 108), Saddle (0, 0)

d o main - x^{2} + 8 x - 12

a sy m pt o t es f (x) = x^{3} - 2

in v erse f (x) = 3 x - 6

in v erse f (x) = \frac{1}{5} x - 1

in v erse 8 - 3 e^{x}

What is the extreme f(x)=4x^4+16x^3 ?
The extreme f(x)=4x^4+16x^3 is Minimum(-3,-108),Saddle(0,0)