Establish the inequality e^(x)<= 1/(1-x) for all x<1. A note in my book says to interpret as a monotonicity statement about the function f(x)=(1-x)e^x.
Here is what I have so far:
e^(x)<= 1/(1-x) becomes (1-x)e^x<=1
The derivative of (1-x)e^x is (1-x)e^(x)+(-1)e^x=-xe^x.
Is this all correct so far? I am not sure where to go with this problem now. Help please!