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

The extreme f(x)=3x^4+16x^3 is Minimum(-4,-256),Saddle(0,0)

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

extreme points

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

Minimum (- 4, - 256), Saddle (0, 0)

Solution steps

f^{'} (x) = 12 x^{3} + 48 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

3 x^{4} + 16 x^{3} : - 256

Minimum (- 4, - 256)

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- 4, - 256), Saddle (0, 0)

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

f (x) = (x - 1) e^{x}

\frac{x ^{2} + 1}{x ^{2} - 4}

f (x, y) = - x^{2} - y^{2} + 8 x + 6 y

f (x) = x + e^{- 2 x}

What is the extreme f(x)=3x^4+16x^3 ?
The extreme f(x)=3x^4+16x^3 is Minimum(-4,-256),Saddle(0,0)