What is the extreme f(x)=3x^4+12x^3 ?

The extreme f(x)=3x^4+12x^3 is Minimum(-3,-81),Saddle(0,0)

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extreme f(x)=3x^4+12x^3

extreme points

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

Minimum (- 3, - 81), Saddle (0, 0)

Solution steps

f^{'} (x) = 12 x^{3} + 36 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

3 x^{4} + 12 x^{3} : - 81

Minimum (- 3, - 81)

Plug

x = 0

into

3 x^{4} + 12 x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 81), Saddle (0, 0)

a sy m pt o t es \frac{5 e ^{x}}{e ^{x} - 9}

d o main f (x) = \frac{( x - 2 )}{( x + 3 )}

in v erse f (x) = x^{2} - 5, x \geq 0

d o main \frac{x - 6}{x ^{2} - 36}

d o main f (x) = - 3 x^{2} + 5

What is the extreme f(x)=3x^4+12x^3 ?
The extreme f(x)=3x^4+12x^3 is Minimum(-3,-81),Saddle(0,0)