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Popular >

extreme f(x)=4x^3-50x^2+150x

Solution

extreme points

f (x) = 4 x^{3} - 50 x^{2} + 150 x

Solution

Maximum (\frac{5 ( 5 - 7 )}{6}, 125 (5 - 7) + \frac{4250 7 - 15625}{27}), Minimum (\frac{5 ( 5 + 7 )}{6}, 125 (5 + 7) + \frac{- 15625 - 4250 7}{27})

Solution steps

f^{'} (x) = 12 x^{2} - 100 x + 150

Find intervals:

Increasing

: - \infty < x < \frac{- 5 7 + 25}{6},

Decreasing

: \frac{- 5 7 + 25}{6} < x < \frac{5 7 + 25}{6},

Increasing

: \frac{5 7 + 25}{6} < x < \infty

Plug

x = \frac{5 ( 5 - 7 )}{6}

into

4 x^{3} - 50 x^{2} + 150 x : 125 (5 - 7) + \frac{4250 7 - 15625}{27}

Maximum (\frac{5 ( 5 - 7 )}{6}, 125 (5 - 7) + \frac{4250 7 - 15625}{27})

Plug

x = \frac{5 ( 5 + 7 )}{6}

into

4 x^{3} - 50 x^{2} + 150 x : 125 (5 + 7) + \frac{- 15625 - 4250 7}{27}

Minimum (\frac{5 ( 5 + 7 )}{6}, 125 (5 + 7) + \frac{- 15625 - 4250 7}{27})

Maximum (\frac{5 ( 5 - 7 )}{6}, 125 (5 - 7) + \frac{4250 7 - 15625}{27}), Minimum (\frac{5 ( 5 + 7 )}{6}, 125 (5 + 7) + \frac{- 15625 - 4250 7}{27})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-50x^2+150x ?
The extreme f(x)=4x^3-50x^2+150x is