How do I approach this derivative problem?

Question

I'm currently studying derivatives in Calculus, but I have no idea how to even approach this problem. Could someone lead me in the right direction without giving the answer?

Question: Assume that f ' (c) = 3. Find the value of f ' (-c) if: f is an odd function, and if f is an even function.

I don't even understand why odd and even functions are included...

Answer 1

It's a trick question. The variable c doesn't even appear in the function f'(c), so f'(-c) is 3 regardless of what you put in the variable.

And incidentally, f cannot possibly be an even function: if f'(c)=3, then f(c)=3c+C, where C is an arbitrary constant of integration. This function is odd iff C=0, and neither even nor odd if C≠0.

Answer 2

try determining whether the derivative f' is also odd when f is odd, and whether the derivative f' is also even when f is even. or maybe, the derivative f' is odd when f is even, and the derivative f' is even when f is odd.

Answer 3

The first answer is correct.

Answer 4

Even: f(-n) = f(n)

Odd f(-n) = -f(n)

if f is even, then f'(c) = -f'(-c). So, if f is even f'(-c) = -3

if f is odd f'(c) = f'(-c). So if f is odd f'(-c) = 3