Derivative and Applications Question

Let's say f satisfies:

**f''(x) + f'(x)g(x) - f(x) = 0**

Show that if **f** is 0 at 2 points, then **f** is 0 in some interval in between them

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How would you start approaching this problem? I tried just trying to do some manipulations with f(x) = f''(x) + f'(x)g(x) and in this case then if f(a) = f''(a) + f'(a)g(a) = 0 and f(b) = f''(b) + f'(b)g(b) = 0 and trying to find some intervals, but I haven't had much luck.

Any help is appreciated, thanks!

RE:Derivative and Applications Question

What is g(x)?

There must be a condition for g(x)!

For example, g(x) could not be a function like -2*tan(x)

Because...if it is, we have a solution that f(x) = sin(x), which is not satisfy "if **f** is 0 at 2 points, then **f** is 0 in some interval in between them"

Bao Q. Ta

PhD Fellow

in Micro-Nanotechnology