Graph Intersections: f'(x) > g'(x) - Can It Intersect More Than Once?

[haxan7]

First of all i am new to this forum, and since my question is from my exam i did not post in homework section, if posted it in wrong section then kindly move it to right one.

So i had this mcq in exam it said that if f'(x)>g'(x) for all values of x.
then the graphs of two function intersect at.
(a) At only one point
(b)Many intersect more than once.

There were other options too but i did not mention them here because i know they were wrong.

I know that the graphs will intersect once, i want to know if it can intersect more than once.

Please also give your reasoning.

 

[vivek.iitd]

The graphs can intersect only once.

 

[vivek.iitd]

because the slopes will not follow the similar inequality, if they are intersecting more than once.

 

[vivek.iitd]

You can think of it from a physics point of view. f'(x)>g'(x) means that rate of change of f(x) is always faster than g(x), once they intersect, the curve g(x) cannot meet f(x) unless until the rate of change of g(x) is greater than f(x) i.e. g'(x)>f'(x) which contradicts our original statement.

 

[haxan7]

You can think of it from a physics point of view. f'(x)>g'(x) means that rate of change of f(x) is always faster than g(x), once they intersect, the curve g(x) cannot meet f(x) unless until the rate of change of g(x) is greater than f(x) i.e. g'(x)>f'(x) which contradicts our original statement.

Yeah got it, thanks