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

The extreme f(x)=x+x^2-x^3 is Minimum(-1/3 ,-5/27),Maximum(1,1)

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

extreme points

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

Minimum (- \frac{1}{3}, - \frac{5}{27}), Maximum (1, 1)

Solution steps

f^{'} (x) = 1 + 2 x - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{3},

Increasing

: - \frac{1}{3} < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

x + x^{2} - x^{3} : - \frac{5}{27}

Minimum (- \frac{1}{3}, - \frac{5}{27})

Plug

x = 1

into

x + x^{2} - x^{3} : 1

Maximum (1, 1)

Minimum (- \frac{1}{3}, - \frac{5}{27}), Maximum (1, 1)

f (x) = e^{x + y}

f (x) = 6 x^{3} - 15 x^{2} + 12 x - 6

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

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

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

What is the extreme f(x)=x+x^2-x^3 ?
The extreme f(x)=x+x^2-x^3 is Minimum(-1/3 ,-5/27),Maximum(1,1)