By condition of tangance df/dx x dg/dx = -1
so
So g(x) is tangent to f(x) at point
Now for x = \ln k
you cordinates of both curve should be same
so x = \ln k satisfies
solve for k
I have a problem that I do not know how to start. If anyone could give me a hint on how to start it, that would be great.
Let be the function given by , and let be the function given by , where is the nonzero constant such that the graph of is tangent to the graph of .
Find the x-coordinate of the point of tangency and the value of .
Hello CursedFirst, you need to find the value of where the two graphs meet: that is where , or
(1)
Then if is a tangent to for this value of , their gradients are equal at this point. So or:
(2)
Now you can use (2) to eliminate the term in (1), and solve the resulting equation for . This is the -coordinate of the point of tangency, which you can then use to find the value of , by substituting it back into (1).
Can you complete it now?
Grandad