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Popular >

extreme-4x^3+200x^2-3000x+17000

Solution

extreme points

- 4 x^{3} + 200 x^{2} - 3000 x + 17000

Solution

Minimum (\frac{5 ( 10 - 10 )}{3}, \frac{1000000 - 145000 10}{27} + 500010 - 33000), Maximum (\frac{5 ( 10 + 10 )}{3}, \frac{1000000 + 145000 10}{27} - 33000 - 500010)

Solution steps

f^{'} (x) = - 12 x^{2} + 400 x - 3000

Find intervals:

Decreasing

: - \infty < x < \frac{- 5 10 + 50}{3},

Increasing

: \frac{- 5 10 + 50}{3} < x < \frac{5 10 + 50}{3},

Decreasing

: \frac{5 10 + 50}{3} < x < \infty

Plug

x = \frac{5 ( 10 - 10 )}{3}

into

- 4 x^{3} + 200 x^{2} - 3000 x + 17000 : \frac{1000000 - 145000 10}{27} + 500010 - 33000

Minimum (\frac{5 ( 10 - 10 )}{3}, \frac{1000000 - 145000 10}{27} + 500010 - 33000)

Plug

x = \frac{5 ( 10 + 10 )}{3}

into

- 4 x^{3} + 200 x^{2} - 3000 x + 17000 : \frac{1000000 + 145000 10}{27} - 33000 - 500010

Maximum (\frac{5 ( 10 + 10 )}{3}, \frac{1000000 + 145000 10}{27} - 33000 - 500010)

Minimum (\frac{5 ( 10 - 10 )}{3}, \frac{1000000 - 145000 10}{27} + 500010 - 33000), Maximum (\frac{5 ( 10 + 10 )}{3}, \frac{1000000 + 145000 10}{27} - 33000 - 500010)

Popular Examples

extreme f(x)=-x+10 extreme points

f (x) = - x + 10

extreme f(x)=-5t^2+61t+18 extreme points

f (x) = - 5 t^{2} + 61 t + 18

extreme f(x,y)=x^2+y^2-30 extreme points

f (x, y) = x^{2} + y^{2} - 30

extreme f(x)=(x^3)/3-(x^2)/2-2x+1 extreme points

f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 2 x + 1

extreme f(x)=(x^3)/3-(x^2)/2-2x+2 extreme points

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

Frequently Asked Questions (FAQ)

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