What is the extreme f(x)=-2x^3+9x^2+168x+69 ?

The extreme f(x)=-2x^3+9x^2+168x+69 is Minimum(-4,-331),Maximum(7,1000)

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extreme f(x)=-2x^3+9x^2+168x+69

extreme points

f (x) = - 2 x^{3} + 9 x^{2} + 168 x + 69

Minimum (- 4, - 331), Maximum (7, 1000)

Solution steps

f^{'} (x) = - 6 x^{2} + 18 x + 168

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = - 4

into

- 2 x^{3} + 9 x^{2} + 168 x + 69 : - 331

Minimum (- 4, - 331)

Plug

x = 7

into

- 2 x^{3} + 9 x^{2} + 168 x + 69 : 1000

Maximum (7, 1000)

Minimum (- 4, - 331), Maximum (7, 1000)

U (x, y) = (x + \frac{x}{y}) (2 y + 3)

- e^{- x} x

\frac{2680}{3725}

f (x) = 3 x^{2} - 6 x + 5

f (x) = 3 x^{2} - 6 x + 9

What is the extreme f(x)=-2x^3+9x^2+168x+69 ?
The extreme f(x)=-2x^3+9x^2+168x+69 is Minimum(-4,-331),Maximum(7,1000)