Help with calculus please!

Question

 How do Curves A and B compare to each other with respect to f and f ′?

 

Question options:

1)	The answer cannot be determined.
2)	f: Curve B, f ′: Curve A
3)	f: Curve A, f ′: Curve B
4)	Neither Curve A or Curve B are derivatives of each other.

Answer 1

These curves appear to be unrelated, lending answer D.

The derivative (called f') tells us the slope of f. So when f is horizontal, as it is at 0.2, the derivative should be equal to 0 (meaning it should be crossing the x axis). However, when A is 0.2, B is not crossing the X axis.

As for the other way around, the sign of the derivative tells us if the function is increasing or decreasing. B is increasing, for example, from 0 to 0.2. However, in that range, the derivative is still negative, which would indicate that f is actually degreasing. So neither function is the derivative of the other.