What is the extreme f(x)=4+x+x^2-x^3 ?

The extreme f(x)=4+x+x^2-x^3 is Minimum(-1/3 , 103/27),Maximum(1,5)

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extreme f(x)=4+x+x^2-x^3

extreme points

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

Minimum (- \frac{1}{3}, \frac{103}{27}), Maximum (1, 5)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

4 + x + x^{2} - x^{3} : \frac{103}{27}

Minimum (- \frac{1}{3}, \frac{103}{27})

Plug

x = 1

into

4 + x + x^{2} - x^{3} : 5

Maximum (1, 5)

Minimum (- \frac{1}{3}, \frac{103}{27}), Maximum (1, 5)

4 x + 5

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

f (x) = 2 x + 1

f (x) = - \frac{2}{3} lo g_{10} (x - 1) + 2

What is the extreme f(x)=4+x+x^2-x^3 ?
The extreme f(x)=4+x+x^2-x^3 is Minimum(-1/3 , 103/27),Maximum(1,5)