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

The extreme f(x)=x^4+x^3-9 is Minimum(-3/4 ,-27/256-9),Saddle(0,-9)

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

extreme points

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

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9), Saddle (0, - 9)

Solution steps

f^{'} (x) = 4 x^{3} + 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{4},

Increasing

: - \frac{3}{4} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{4}

into

x^{4} + x^{3} - 9 : - \frac{27}{256} - 9

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9)

Plug

x = 0

into

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

Saddle (0, - 9)

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9), Saddle (0, - 9)

f (x, y) = x^{3} + y^{3} - 30 x y

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

f (x) = - x^{3} + 3 x + 1

f (x, y) = x^{2} + x y + y^{2} - 3 x

- x^{3} - 3 x^{2}

What is the extreme f(x)=x^4+x^3-9 ?
The extreme f(x)=x^4+x^3-9 is Minimum(-3/4 ,-27/256-9),Saddle(0,-9)