Thread: Question from Calculus Mid

Given f(x) and g(x), where f'(x) > g'(x) at all points, how many times can the two funtions intersect?
(i) Exactly Once
(ii) More than Once

Originally Posted by sk9190

Given f(x) and g(x), where f'(x) > g'(x) at all points, how many times can the two funtions intersect?
(i) Exactly Once
(ii) More than Once

Consider how many x-intercepts a graph of the function y = f(x) - g(x) can have ....

I'm not sure I follow. Can you elaborate?

Originally Posted by mr fantastic

Consider how many x-intercepts a graph of the function y = f(x) - g(x) can have ....

Well, if y = f(x) - g(x), what do you know about dy/dx and what implications does that have on the number of x-intercepts that y has ....?

I'm thinking the answer is Exactly once and all the possible functions for f and g that I can think of support this, but I don't understand the basic principle as to why

Originally Posted by sk9190

I'm thinking the answer is Exactly once and all the possible functions for f and g that I can think of support this, but I don't understand the basic principle as to why

Then you need to reflect on what I posted for more than just a handful of minutes.

Alright, I'm giving it 10 minutes, but if I can't figure it out then can you just spell it out for me? =P

Originally Posted by sk9190

Alright, I'm giving it 10 minutes, but if I can't figure it out then can you just spell it out for me? =P

You know that dy/dx = f'(x) - g'(x) > 0 for all values of x. Now think about what dy/dx > 0 means in terms of the behaviour of the graph.