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Popular Functions >

extreme f(x)=4x^3-80x^2+300x

Solution

extreme points

f (x) = 4 x^{3} - 80 x^{2} + 300 x

Solution

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27}), Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

Solution steps

f^{'} (x) = 12 x^{2} - 160 x + 300

Find intervals:

Increasing

: - \infty < x < \frac{- 5 7 + 20}{3},

Decreasing

: \frac{- 5 7 + 20}{3} < x < \frac{5 7 + 20}{3},

Increasing

: \frac{5 7 + 20}{3} < x < \infty

Plug

x = \frac{5 ( 4 - 7 )}{3}

into

4 x^{3} - 80 x^{2} + 300 x : 500 (4 - 7) + \frac{20500 7 - 64000}{27}

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27})

Plug

x = \frac{5 ( 4 + 7 )}{3}

into

4 x^{3} - 80 x^{2} + 300 x : 500 (4 + 7) + \frac{- 64000 - 20500 7}{27}

Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

Maximum (\frac{5 ( 4 - 7 )}{3}, 500 (4 - 7) + \frac{20500 7 - 64000}{27}), Minimum (\frac{5 ( 4 + 7 )}{3}, 500 (4 + 7) + \frac{- 64000 - 20500 7}{27})

Graph

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Frequently Asked Questions (FAQ)

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