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Popular Functions >

extreme-80e^x+2xe^x+2x^2e^x-1

Solution

extreme

Solution

Maximum (\frac{- 3 - 165}{2}, 4 e^{\frac{- 3 - 165}{2}} + 2165 e^{\frac{- 3 - 165}{2}} - 1), Minimum (\frac{- 3 + 165}{2}, 4 e^{\frac{- 3 + 165}{2}} - 2165 e^{\frac{- 3 + 165}{2}} - 1)

Solution steps

f^{'} (x) = 2 e^{x} (x^{2} + 3 x - 39)

Find intervals:

Increasing

: - \infty < x < \frac{- 165 - 3}{2},

Decreasing

: \frac{- 165 - 3}{2} < x < \frac{- 3 + 165}{2},

Increasing

: \frac{- 3 + 165}{2} < x < \infty

Plug

x = \frac{- 3 - 165}{2}

into

- 80 e^{x} + 2 x e^{x} + 2 x^{2} e^{x} - 1 : 4 e^{\frac{- 3 - 165}{2}} + 2165 e^{\frac{- 3 - 165}{2}} - 1

Maximum (\frac{- 3 - 165}{2}, 4 e^{\frac{- 3 - 165}{2}} + 2165 e^{\frac{- 3 - 165}{2}} - 1)

Plug

x = \frac{- 3 + 165}{2}

into

- 80 e^{x} + 2 x e^{x} + 2 x^{2} e^{x} - 1 : 4 e^{\frac{- 3 + 165}{2}} - 2165 e^{\frac{- 3 + 165}{2}} - 1

Minimum (\frac{- 3 + 165}{2}, 4 e^{\frac{- 3 + 165}{2}} - 2165 e^{\frac{- 3 + 165}{2}} - 1)

Maximum (\frac{- 3 - 165}{2}, 4 e^{\frac{- 3 - 165}{2}} + 2165 e^{\frac{- 3 - 165}{2}} - 1), Minimum (\frac{- 3 + 165}{2}, 4 e^{\frac{- 3 + 165}{2}} - 2165 e^{\frac{- 3 + 165}{2}} - 1)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme-80e^x+2xe^x+2x^2e^x-1 ?
The extreme-80e^x+2xe^x+2x^2e^x-1 is