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Popular >

extreme y=-12x^5-45x^4+20x^3-1

Solution

extreme points

y = - 12 x^{5} - 45 x^{4} + 20 x^{3} - 1

Solution

Minimum (\frac{- 3 - 13}{2}, - \frac{3 ( 213 + 59 13 )}{2} - 361 - 10013), Saddle (0, - 1), Maximum (\frac{- 3 + 13}{2}, \frac{3 ( 59 13 - 213 )}{2} + 10013 - 361)

Solution steps

f^{'} (x) = - 60 x^{4} - 180 x^{3} + 60 x^{2}

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 13}{2},

Increasing

: \frac{- 3 - 13}{2} < x < 0,

Increasing

: 0 < x < \frac{13 - 3}{2},

Decreasing

: \frac{13 - 3}{2} < x < \infty

Plug

x = \frac{- 3 - 13}{2}

into

- 12 x^{5} - 45 x^{4} + 20 x^{3} - 1 : - \frac{3 ( 213 + 59 13 )}{2} - 361 - 10013

Minimum (\frac{- 3 - 13}{2}, - \frac{3 ( 213 + 59 13 )}{2} - 361 - 10013)

Plug

x = 0

into

- 12 x^{5} - 45 x^{4} + 20 x^{3} - 1 : - 1

Saddle (0, - 1)

Plug

x = \frac{- 3 + 13}{2}

into

- 12 x^{5} - 45 x^{4} + 20 x^{3} - 1 : \frac{3 ( 59 13 - 213 )}{2} + 10013 - 361

Maximum (\frac{- 3 + 13}{2}, \frac{3 ( 59 13 - 213 )}{2} + 10013 - 361)

Minimum (\frac{- 3 - 13}{2}, - \frac{3 ( 213 + 59 13 )}{2} - 361 - 10013), Saddle (0, - 1), Maximum (\frac{- 3 + 13}{2}, \frac{3 ( 59 13 - 213 )}{2} + 10013 - 361)

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Frequently Asked Questions (FAQ)

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