# Thread: Curve Sketching proof.

1. ## Curve Sketching proof.

Prove that a function of the form f(x)= (ax)/(bx+c), where a, b, and c are non-zero constants, will never have a turning point. I am assuming by turning point, they mean a local max or min or an inflection point, but I'm not sure to where to go from there.

2. ## Re: Curve Sketching proof.

Yes, a turning point is where the derivative changes from positive to negative or vice versa. Of course, to do that, the derivative must be 0 at that point (the derivative of a differentiable function is not necessarily continuous everywhere but it must satify the "intermediate value property" at every point so in order to change from postitive to negative or vice versa, it must pass through 0).

So find the derivative of your function and set it equal to 0. That alone is not enough; once you have found "candidate" points you must show that the derivative really does change sign- doesn't just go from a positive value to 0 and then become positive again.