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Popular >

extreme f(x)=x^3-5x^2+6x

Solution

extreme points

f (x) = x^{3} - 5 x^{2} + 6 x

Solution

Maximum (\frac{5 - 7}{3}, 2 (5 - 7) + \frac{68 7 - 250}{27}), Minimum (\frac{5 + 7}{3}, 2 (5 + 7) + \frac{- 250 - 68 7}{27})

Solution steps

f^{'} (x) = 3 x^{2} - 10 x + 6

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = \frac{5 - 7}{3}

into

x^{3} - 5 x^{2} + 6 x : 2 (5 - 7) + \frac{68 7 - 250}{27}

Maximum (\frac{5 - 7}{3}, 2 (5 - 7) + \frac{68 7 - 250}{27})

Plug

x = \frac{5 + 7}{3}

into

x^{3} - 5 x^{2} + 6 x : 2 (5 + 7) + \frac{- 250 - 68 7}{27}

Minimum (\frac{5 + 7}{3}, 2 (5 + 7) + \frac{- 250 - 68 7}{27})

Maximum (\frac{5 - 7}{3}, 2 (5 - 7) + \frac{68 7 - 250}{27}), Minimum (\frac{5 + 7}{3}, 2 (5 + 7) + \frac{- 250 - 68 7}{27})

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Frequently Asked Questions (FAQ)

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