What is the inflection f(x)=e^xsqrt(x) ?

The inflection f(x)=e^xsqrt(x) is ((-1+sqrt(2))/2 ,e^{(-1+sqrt(2))/2}sqrt((-1+\sqrt{2))/2})

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inflection f(x)=e^xsqrt(x)

inflection points

f (x) = e^{x} x

\frac{- 1 + 2}{2}, e^{\frac{- 1 + 2}{2}} \frac{- 1 + 2}{2}

Solution steps

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

Find intervals:

Concave Downward

: 0 < x < \frac{1}{2} - \frac{1}{2},

Concave Upward

: \frac{1}{2} - \frac{1}{2} < x < \infty

Plug

x = \frac{- 1 + 2}{2}

into

e^{x} x : e^{\frac{- 1 + 2}{2}} \frac{- 1 + 2}{2}

\frac{- 1 + 2}{2}, e^{\frac{- 1 + 2}{2}} \frac{- 1 + 2}{2}

f (x) = - 4 x^{2} - x^{3}

f (x) = ln (e^{x} - 4)

ln (\frac{1}{2})

f (x) = x + 4

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

What is the inflection f(x)=e^xsqrt(x) ?
The inflection f(x)=e^xsqrt(x) is ((-1+sqrt(2))/2 ,e^{(-1+sqrt(2))/2}sqrt((-1+\sqrt{2))/2})