Here's the question:
I don't know how to proceed.
First thing we do know about these curves, is that both have the point (1,0)
Let
Let
We have, when x = 1, y = 0. so for the following happens:
..............(1)
similarly, for , the following happens:
So we know the value of c, and we know one equation that relates a and b. but what else do we know?
they share a common tangent at (1,0), in particular, the slope of the tangent line at x = 1 is the same for the two curves
so, , when x = 1, we get:
and
, when x = 1, we get:
Now we equate the two slopes:
...............(2)
............since
But from equation (1),
So,