What is the inflection f(x)=(5-e^x)^2 ?

The inflection f(x)=(5-e^x)^2 is (ln(5)-ln(2), 25/4)

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inflection f(x)=(5-e^x)^2

inflection points

f (x) = (5 - e^{x})^{2}

(ln (5) - ln (2), \frac{25}{4})

Solution steps

f^{''} (x) = - 2 (5 e^{x} - 2 e^{2 x})

Find intervals:

Concave Downward

: - \infty < x < ln (\frac{5}{2}),

Concave Upward

: ln (\frac{5}{2}) < x < \infty

Plug

x = ln (5) - ln (2)

into

(5 - e^{x})^{2} : \frac{25}{4}

(ln (5) - ln (2), \frac{25}{4})

What is the inflection f(x)=(5-e^x)^2 ?
The inflection f(x)=(5-e^x)^2 is (ln(5)-ln(2), 25/4)