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Popular >

extreme f(x)=4x^3-60x^2+200x

Solution

extreme points

f (x) = 4 x^{3} - 60 x^{2} + 200 x

Solution

Maximum (\frac{5 ( 3 - 3 )}{3}, - 1000 (2 - 3) + \frac{18000 - 8000 3}{9}), Minimum (\frac{5 ( 3 + 3 )}{3}, - 1000 (2 + 3) + \frac{18000 + 8000 3}{9})

Solution steps

f^{'} (x) = 12 x^{2} - 120 x + 200

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

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

into

4 x^{3} - 60 x^{2} + 200 x : - 1000 (2 - 3) + \frac{18000 - 8000 3}{9}

Maximum (\frac{5 ( 3 - 3 )}{3}, - 1000 (2 - 3) + \frac{18000 - 8000 3}{9})

Plug

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

into

4 x^{3} - 60 x^{2} + 200 x : - 1000 (2 + 3) + \frac{18000 + 8000 3}{9}

Minimum (\frac{5 ( 3 + 3 )}{3}, - 1000 (2 + 3) + \frac{18000 + 8000 3}{9})

Maximum (\frac{5 ( 3 - 3 )}{3}, - 1000 (2 - 3) + \frac{18000 - 8000 3}{9}), Minimum (\frac{5 ( 3 + 3 )}{3}, - 1000 (2 + 3) + \frac{18000 + 8000 3}{9})

Popular Examples

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extreme f(x)=x^3-x^2-x+5,-1<= x<= 2 extreme points

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-60x^2+200x ?
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