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Popular Functions >

extreme-t^3+21t^2+35t+20

Solution

extreme

Solution

Minimum (- \frac{- 21 + 546}{3}, \frac{518 546 - 12348}{9} + 2323 - 98546), Maximum (\frac{21 + 546}{3}, \frac{- 12348 - 518 546}{9} + 2323 + 98546)

Solution steps

f^{'} (t) = - 3 t^{2} + 42 t + 35

Find intervals:

Decreasing

: - \infty < t < - \frac{182}{3} + 7,

Increasing

: - \frac{182}{3} + 7 < t < \frac{182}{3} + 7,

Decreasing

: \frac{182}{3} + 7 < t < \infty

Plug

t = - \frac{- 21 + 546}{3}

into

- t^{3} + 21 t^{2} + 35 t + 20 : \frac{518 546 - 12348}{9} + 2323 - 98546

Minimum (- \frac{- 21 + 546}{3}, \frac{518 546 - 12348}{9} + 2323 - 98546)

Plug

t = \frac{21 + 546}{3}

into

- t^{3} + 21 t^{2} + 35 t + 20 : \frac{- 12348 - 518 546}{9} + 2323 + 98546

Maximum (\frac{21 + 546}{3}, \frac{- 12348 - 518 546}{9} + 2323 + 98546)

Minimum (- \frac{- 21 + 546}{3}, \frac{518 546 - 12348}{9} + 2323 - 98546), Maximum (\frac{21 + 546}{3}, \frac{- 12348 - 518 546}{9} + 2323 + 98546)

Graph

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Frequently Asked Questions (FAQ)

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