What is the extreme f(x)=3x^4+9x^3+11 ?

The extreme f(x)=3x^4+9x^3+11 is Minimum(-9/4 ,-3745/256),Saddle(0,11)

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extreme f(x)=3x^4+9x^3+11

extreme points

f (x) = 3 x^{4} + 9 x^{3} + 11

Minimum (- \frac{9}{4}, - \frac{3745}{256}), Saddle (0, 11)

Solution steps

f^{'} (x) = 12 x^{3} + 27 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{9}{4},

Increasing

: - \frac{9}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{9}{4}

into

3 x^{4} + 9 x^{3} + 11 : - \frac{3745}{256}

Minimum (- \frac{9}{4}, - \frac{3745}{256})

Plug

x = 0

into

3 x^{4} + 9 x^{3} + 11 : 11

Saddle (0, 11)

Minimum (- \frac{9}{4}, - \frac{3745}{256}), Saddle (0, 11)

What is the extreme f(x)=3x^4+9x^3+11 ?
The extreme f(x)=3x^4+9x^3+11 is Minimum(-9/4 ,-3745/256),Saddle(0,11)