the slope of the curve y= (x^2) - e^-x at its point of inflection is?

Answer 1

y' = 2x + e^-x; y'' = 2 - e^{- x} = 0 to get point of inflection; e^{- x} = 2; x = - ln2, y(-ln2) = ln²2 - 2;

Point of inflection (- ln2, ln²2 - 2)

Slope of curve at this point is y'(-ln2) = - 2ln2 + 2