What is the inflection f(x)=e^{-2x}-x^2 ?

The inflection f(x)=e^{-2x}-x^2 is ((ln(2))/2 , 1/2-(ln^2(2))/4)

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inflection f(x)=e^{-2x}-x^2

inflection points

f (x) = e^{- 2 x} - x^{2}

(\frac{ln ( 2 )}{2}, \frac{1}{2} - \frac{ln ^{2} ( 2 )}{4})

Solution steps

f^{''} (x) = 4 e^{- 2 x} - 2

Find intervals:

Concave Upward

: - \infty < x < \frac{ln ( 2 )}{2},

Concave Downward

: \frac{ln ( 2 )}{2} < x < \infty

Plug

x = \frac{ln ( 2 )}{2}

into

e^{- 2 x} - x^{2} : \frac{1}{2} - \frac{ln ^{2} ( 2 )}{4}

(\frac{ln ( 2 )}{2}, \frac{1}{2} - \frac{ln ^{2} ( 2 )}{4})

What is the inflection f(x)=e^{-2x}-x^2 ?
The inflection f(x)=e^{-2x}-x^2 is ((ln(2))/2 , 1/2-(ln^2(2))/4)