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Popular >

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})

Popular Examples

asymptotes of f(x)=(x^2)/(x^2+2)asymptotes

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

asymptotes of ln(x+4)asymptotes

ln (x + 4)

domain of (x^2+x-2)/(x^2-3x-4)domain

\frac{x ^{2} + x - 2}{x ^{2} - 3 x - 4}

domain of f(x)=log_{4}(x-4)domain

f (x) = lo g_{4} (x - 4)

inverse of f(x)=4x^2+8x-20 inverse

f (x) = 4 x^{2} + 8 x - 20

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-80x^2+300x ?
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