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Popular >

extreme-x^3+x^2+x+8

Solution

extreme points

- x^{3} + x^{2} + x + 8

Solution

Minimum (- \frac{1}{3}, \frac{211}{27}), Maximum (1, 9)

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

- x^{3} + x^{2} + x + 8 : \frac{211}{27}

Minimum (- \frac{1}{3}, \frac{211}{27})

Plug

x = 1

into

- x^{3} + x^{2} + x + 8 : 9

Maximum (1, 9)

Minimum (- \frac{1}{3}, \frac{211}{27}), Maximum (1, 9)

Popular Examples

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extreme f(x)=200x-(0.003x^2+80x+500000)extreme points

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f (x, y) = x \cdot e^{y}

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Frequently Asked Questions (FAQ)

What is the extreme-x^3+x^2+x+8 ?
The extreme-x^3+x^2+x+8 is Minimum(-1/3 , 211/27),Maximum(1,9)