What is the extreme-(2e^x)/(-4x-1) ?

The extreme-(2e^x)/(-4x-1) is Minimum(3/4 ,(e^{3/4})/2)

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extreme-(2e^x)/(-4x-1)

extreme

Minimum (\frac{3}{4}, \frac{e ^{\frac{3}{4}}}{2})

Solution steps

f^{'} (x) = - \frac{2 ( - 4 e ^{x} x + 3 e ^{x} )}{( - 4 x - 1 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - \frac{1}{4},

Decreasing

: - \frac{1}{4} < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < \infty

Plug

x = \frac{3}{4}

into

- \frac{2 e ^{x}}{- 4 x - 1} : \frac{e ^{\frac{3}{4}}}{2}

Minimum (\frac{3}{4}, \frac{e ^{\frac{3}{4}}}{2})

What is the extreme-(2e^x)/(-4x-1) ?
The extreme-(2e^x)/(-4x-1) is Minimum(3/4 ,(e^{3/4})/2)