What is the extreme f(x)=6x^3+x^2-2 ?

The extreme f(x)=6x^3+x^2-2 is Maximum(-1/9 ,-485/243),Minimum(0,-2)

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extreme f(x)=6x^3+x^2-2

extreme points

f (x) = 6 x^{3} + x^{2} - 2

Maximum (- \frac{1}{9}, - \frac{485}{243}), Minimum (0, - 2)

Solution steps

f^{'} (x) = 18 x^{2} + 2 x

Find intervals:

Increasing

: - \infty < x < - \frac{1}{9},

Decreasing

: - \frac{1}{9} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{1}{9}

into

6 x^{3} + x^{2} - 2 : - \frac{485}{243}

Maximum (- \frac{1}{9}, - \frac{485}{243})

Plug

x = 0

into

6 x^{3} + x^{2} - 2 : - 2

Minimum (0, - 2)

Maximum (- \frac{1}{9}, - \frac{485}{243}), Minimum (0, - 2)

f (x, y) = x^{2} - 4 x y + 5 y^{2} + 2 x + 4 y - 4

f (x) = 1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}}

f (x, y) = x^{3} - 3 x + y^{2} - 4 y

0.0025 x^{4} + 0.5 x^{3} - 8 x^{2} + 1000

f (x, y) = x^{2} + 6 x + y^{3} - 6 y^{2}

What is the extreme f(x)=6x^3+x^2-2 ?
The extreme f(x)=6x^3+x^2-2 is Maximum(-1/9 ,-485/243),Minimum(0,-2)