If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x, then the graphs of y = f(x) and y = g(x)...
Came up on my calculus test, and it's the only one I can't get.
a) intersect exactly once
b) intersect no more than once
c) do not intersect
d) could intersect more than once
e) have a common tangent at each point of intersection
what's with the poll? you do math by majority opinion? one of the beautiful things about math is that it is objective. opinions don't matter!
obviously they can't have a common tangent, since the slopes are always different.
so reason through the others.
(a) do they have to intersect once?
consider $\displaystyle f(x) = e^x$ and $\displaystyle g(x) = -1$
(b) do they have to intersect more than once?
consider the same example above
(c) do they have to not intersect?
...come up with your own example of why or why not.
do the same for choice (d)
what do you come up with?