I need to solve for all values of a the number of solutions to the equation
So far, and I'm very, very unsure about this, I've got:
We set f(x) = e^x / x and derive, ending up with
meaning that the curve changes at x = 1.
We put up a value? table
x | 0 1
f'(x) | ~ - 0 +
f(x) | ~ e
We look at the limits
So we have a curve with its minimum point at (1,e).
The solutions are:
a < e has 0 solutions
a = e has 1 solution
a > e has 2 solutions
I forgot to add that we need to check for asymptotes. Since f(x) / x approaches infinity as x->infinity there aren't any asymptotes.