what do we know about the line: ?
it has slope and y-intercept 1
how do we find the slope? by the derivative, so let's find the derivative. i will call the slope m.
ok, now we know that the given line passes through (0,1) and that all points on the curve are given by
thus, the tangent line must pass through the points and
so another formula from the slope is (from precalc):
but we are talking about the same lines here, the slopes must be equal. thus we equate (1) and (2) to obtain:
solving this, we find that
thus, the points any tangent line would go through are:
and ....tangent line 1
and ....tangent line 2
find the two lines that pass through those points and you will find the two values for