**Unformatted text preview: **˜ f ( x ) = x if-1 < x < , if 0 < x < 1 ,-1 2 if x = 1 f ( x + 2) = f ( x ) . Prove that the derivative of an even function is odd. If f is an even function then f (-x ) = f ( x ). Taking the derivative of both sides gives us (using the chain rule)-f (-x ) = f ( x ). In other words, f (-x ) =-f ( x ), and f is thus odd. 1...

View
Full
Document