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

The extreme f(x)=x^3+3x^4 is Minimum(-1/4 ,-1/256),Saddle(0,0)

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

extreme

Minimum (- \frac{1}{4}, - \frac{1}{256}), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{4},

Increasing

: - \frac{1}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{1}{4}

into

x^{3} + 3 x^{4} : - \frac{1}{256}

Minimum (- \frac{1}{4}, - \frac{1}{256})

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- \frac{1}{4}, - \frac{1}{256}), Saddle (0, 0)

What is the extreme f(x)=x^3+3x^4 ?
The extreme f(x)=x^3+3x^4 is Minimum(-1/4 ,-1/256),Saddle(0,0)