What is the extreme-x^3+5x^2+8x+9 ?

The extreme-x^3+5x^2+8x+9 is Minimum(-2/3 , 167/27),Maximum(4,57)

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extreme-x^3+5x^2+8x+9

extreme points

- x^{3} + 5 x^{2} + 8 x + 9

Minimum (- \frac{2}{3}, \frac{167}{27}), Maximum (4, 57)

Solution steps

f^{'} (x) = - 3 x^{2} + 10 x + 8

Find intervals:

Decreasing

: - \infty < x < - \frac{2}{3},

Increasing

: - \frac{2}{3} < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} + 5 x^{2} + 8 x + 9 : \frac{167}{27}

Minimum (- \frac{2}{3}, \frac{167}{27})

Plug

x = 4

into

- x^{3} + 5 x^{2} + 8 x + 9 : 57

Maximum (4, 57)

Minimum (- \frac{2}{3}, \frac{167}{27}), Maximum (4, 57)

- 2 x^{2} + 4 x - 8

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

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

f (x) = 4 x^{2} - 6 x

y = 2 x

What is the extreme-x^3+5x^2+8x+9 ?
The extreme-x^3+5x^2+8x+9 is Minimum(-2/3 , 167/27),Maximum(4,57)