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Popular >

extreme f(x)=-13t^3+18t^2+37t+6

Solution

extreme points

f (x) = - 13 t^{3} + 18 t^{2} + 37 t + 6

Solution

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6), Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

Solution steps

f^{'} (t) = - 39 t^{2} + 36 t + 37

Find intervals:

Decreasing

: - \infty < t < - \frac{589}{13 3} + \frac{6}{13},

Increasing

: - \frac{589}{13 3} + \frac{6}{13} < t < \frac{589}{13 3} + \frac{6}{13},

Decreasing

: \frac{589}{13 3} + \frac{6}{13} < t < \infty

Plug

t = - \frac{- 18 + 1767}{39}

into

- 13 t^{3} + 18 t^{2} + 37 t + 6 : \frac{29862 - 1178 1767}{1521} + 6

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6)

Plug

t = \frac{18 + 1767}{39}

into

- 13 t^{3} + 18 t^{2} + 37 t + 6 : \frac{29862 + 1178 1767}{1521} + 6

Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

Minimum (- \frac{- 18 + 1767}{39}, \frac{29862 - 1178 1767}{1521} + 6), Maximum (\frac{18 + 1767}{39}, \frac{29862 + 1178 1767}{1521} + 6)

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Frequently Asked Questions (FAQ)

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