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

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In summary, the conversation discusses a multiple choice question in an exam about the intersection of two functions based on their derivatives. The correct answer is that the graphs will intersect only once, as the slopes will not follow the same inequality if they intersect more than once. This can be understood from a physics perspective, where the rate of change of one function must be greater than the other for them to intersect.
  • #1
haxan7
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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.
 
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  • #2
The graphs can intersect only once.
 
  • #3
because the slopes will not follow the similar inequality, if they are intersecting more than once.
 
  • #4
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.
 
  • #5
vivek.iitd said:
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
 

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

What is the meaning of "Graph Intersections: f'(x) > g'(x) - Can It Intersect More Than Once?"

Graph intersections refer to the points where two or more graphs intersect each other. The notation "f'(x) > g'(x)" means that the slope of function f is greater than the slope of function g at a specific point. This raises the question of whether these two graphs can intersect at more than one point.

Why is it important to consider intersections of graphs with different slopes?

Intersections of graphs with different slopes can provide valuable information about the relationship between two functions. It can help determine where the functions are increasing, decreasing, or staying constant. It can also reveal any points of intersection, which can be useful in solving equations and identifying critical points.

Can two graphs with the same slope intersect more than once?

Yes, two graphs with the same slope can intersect more than once. This means that at different points, both graphs have the same slope. However, it is also possible for two graphs with the same slope to have no points of intersection.

What happens when the slopes of two graphs are equal at a specific point?

When the slopes of two graphs are equal at a specific point, it means that the two graphs are parallel at that point. This can occur when the functions have the same rate of change at that point. It is important to note that parallel lines never intersect, so the two graphs will not intersect at any other point.

Are there any special cases where two graphs with different slopes can intersect more than once?

Yes, there are special cases where two graphs with different slopes can intersect more than once. For example, if one graph has a sharp turn or a point of discontinuity, it can intersect with the other graph at more than one point. Also, if the two graphs are periodic functions, they can intersect multiple times within a specific interval.

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