But the point is to draw a function with these properties. You just have to have a smooth curve that approaches 0 asymptotically and is concave up. No worries about graphing any particular function!
Either you got the description wrong or I'm especially rusty - in that case, f''(x) = e^(-x), which is positive even when x is negative, so it doesn't always have the same sign.
But the point is to draw a function with these properties. You just have to have a smooth curve that approaches 0 asymptotically and is concave up. No worries about graphing any particular function!