How to solve for x ?
Some trial and error might help here.Originally Posted by totalnewbie
Trial 1
Assume the point is the tangency point on
Then we can find the slope of the tangent at , and
the corresponding value of , which will allow us to find
the equation of the tangent. Now check that this line is a tangent
to , if it is our job is done, if not proceed to Trial 2
Trial 2
Assume the point is the tangency point on ,
then proceed as in Trial 1, but with the roles of and
interchanged.
RonL
Hello,Originally Posted by totalnewbie
if there exists a common tangent then the gradient of both functions must be equal. So first calculate the drivative of both functions:
Both are equal:
Solve for x and you'll get:
Complete the coordinates:
That means that the graphs of both functions have one common point: the tangent point. There exists one tangent (that's a special case, normally there must be two tangents!)
Use the point-slope-formula:
I've attached a drawing to demonstrate my results.
Greetings
EB