Says here, a function f is defined for all real numbers and has the following property: f(a + b) - f(a) = 3(a^2)b + 2b^2. f ' (x) is equal to what?

Basically, are a and b constants or something? How do I find f ' (x)?

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- May 18th 2008, 12:50 PMLeoBloom.derivative of unknown function
Says here, a function f is defined for all real numbers and has the following property: f(a + b) - f(a) = 3(a^2)b + 2b^2. f ' (x) is equal to what?

Basically, are a and b constants or something? How do I find f ' (x)? - May 18th 2008, 01:08 PMSoroban
Hello, LeoBloom!

Quote:

A function is defined for all real and: .

Find

They have given us about half of this defintion: .

Divide by

Take the limit as

. .

So we have: .

Therefore: .

- May 18th 2008, 02:27 PMLeoBloom.
Wow thanks alot, I can't believe I didn't notice how similar it looked to the definition of a derivative.