What is the inflection f(x)=e^x-x^2-2x+6 ?

The inflection f(x)=e^x-x^2-2x+6 is (ln(2),-ln^2(2)-2ln(2)+8)

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inflection f(x)=e^x-x^2-2x+6

inflection points

f (x) = e^{x} - x^{2} - 2 x + 6

(ln (2), - ln^{2} (2) - 2 ln (2) + 8)

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < ln (2),

Concave Upward

: ln (2) < x < \infty

Plug

x = ln (2)

into

e^{x} - x^{2} - 2 x + 6 : - ln^{2} (2) - 2 ln (2) + 8

(ln (2), - ln^{2} (2) - 2 ln (2) + 8)

f (x) = - 3 \cdot 5^{- x + 3}

f (x) = x^{3} + x

- x^{2} - 2 x - 1

f (x) = 0.5 (2)^{x}

x^{2} - 3

What is the inflection f(x)=e^x-x^2-2x+6 ?
The inflection f(x)=e^x-x^2-2x+6 is (ln(2),-ln^2(2)-2ln(2)+8)