- #1

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Basically;

**Define f(x) where the solution to f(x) = f'(x) is the same as the solution to f(x) = ∫f(x)dx, f(x) ≠ e^x and c = 0**

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- Thread starter Saracen Rue
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- #1

- 144

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Basically;

- #2

fresh_42

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What exactly are you looking for?

- #3

- 144

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I'll give an example;

What exactly are you looking for?

Let f(x) = sin^4(x). In this scenario, f(x), f'(x) and ∫f(x)dx all intersect the x-axis at (0, 0). Therefore, there is a three-way intersection between f(x), f'(x) and ∫f(x)dx at said point. I'm looking for other functions or relations which also have a three-way intersection between f(x), f'(x) and ∫f(x)dx. Preferably not at the origin, but I don't mind if they are.

- #4

fresh_42

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How about ##f(x)=(x-a)^n## with ##n > 1##?

- #5

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Yes, that is an excellent example of what I meant. Thank you :)How about ##f(x)=(x-a)^n## with ##n > 1##?

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