What is the extreme-1/3 x^3-5x^2+2000x-326 ?

The extreme-1/3 x^3-5x^2+2000x-326 is Minimum(-50,-213478/3),Maximum(40, 151022/3)

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extreme-1/3 x^3-5x^2+2000x-326

extreme points

- \frac{1}{3} x^{3} - 5 x^{2} + 2000 x - 326

Minimum (- 50, - \frac{213478}{3}), Maximum (40, \frac{151022}{3})

Solution steps

f^{'} (x) = - x^{2} - 10 x + 2000

Find intervals:

Decreasing

: - \infty < x < - 50,

Increasing

: - 50 < x < 40,

Decreasing

: 40 < x < \infty

Plug

x = - 50

into

- \frac{1}{3} x^{3} - 5 x^{2} + 2000 x - 326 : - \frac{213478}{3}

Minimum (- 50, - \frac{213478}{3})

Plug

x = 40

into

- \frac{1}{3} x^{3} - 5 x^{2} + 2000 x - 326 : \frac{151022}{3}

Maximum (40, \frac{151022}{3})

Minimum (- 50, - \frac{213478}{3}), Maximum (40, \frac{151022}{3})

f (x) = x y (10 - 2 x - 3 y)

y^{3} + 3 x^{2} y - 6 x^{2} - 6 y^{2} + 2

f (x) = 3000 x^{2} - 2000 x + 8000

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

\frac{x}{x ^{2} + 49}

What is the extreme-1/3 x^3-5x^2+2000x-326 ?
The extreme-1/3 x^3-5x^2+2000x-326 is Minimum(-50,-213478/3),Maximum(40, 151022/3)