Let be a twice-differentiable function with f'(x)=(x-3)e^ -x

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f

be a twice-differentiable function with

f'(x)=(x-3)e^{-x},\qquad f''(x)=(-x+2)e^{-x}.

Determine the set of all real numbers

x

for which

f

is decreasing and concave up simultaneously.