What is the extreme f(x)=-x^3+x^2+8x+9 ?

The extreme f(x)=-x^3+x^2+8x+9 is Minimum(-4/3 , 67/27),Maximum(2,21)

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extreme f(x)=-x^3+x^2+8x+9

extreme points

f (x) = - x^{3} + x^{2} + 8 x + 9

Minimum (- \frac{4}{3}, \frac{67}{27}), Maximum (2, 21)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 2 < x < \infty

Plug

x = - \frac{4}{3}

into

- x^{3} + x^{2} + 8 x + 9 : \frac{67}{27}

Minimum (- \frac{4}{3}, \frac{67}{27})

Plug

x = 2

into

- x^{3} + x^{2} + 8 x + 9 : 21

Maximum (2, 21)

Minimum (- \frac{4}{3}, \frac{67}{27}), Maximum (2, 21)

f (x) = x^{2} + 5 x - 3

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

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

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

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

What is the extreme f(x)=-x^3+x^2+8x+9 ?
The extreme f(x)=-x^3+x^2+8x+9 is Minimum(-4/3 , 67/27),Maximum(2,21)