Originally Posted by

**HallsofIvy** Yes, that's the chain rule $\displaystyle \frac{df(u(x))}{dx}= \frac{df(u)}{du}\frac{du}{dx}$.

No. The derivative of ln(u) with respect to u is 1/u so with $\displaystyle u= 4x^2+ 5x+ 3$ that is $\displaystyle \frac{1}{4x^2+ 5x+ 3}$. You have an extra "x" in the denominator. You **replace** the denominator by u, not multiply it.

Yes.

Yes! very good.

Not unless you explain **what** she did! I presume she **did** use a specific direction for the initial motion. Either she did not mention it or you didn't notice. It has been my experience that one begins a dive by going **up**. Actually, if you don't want to hit the platform on the way down (remember when that happened to Greg Luganis, one of the greatest divers ever, in the Olympics?), you had better angle your initial motion slightly out from the board!

But since you mention no angles, I suspect your teacher took the easy case of jumping directly up (and then the platform magically disappears!). Your mention of "b/2a" reminds me of completing the square. The equation for height in this situation is a quadratic- its graph is a parabola- and you can find the highest point, the vertex of the parabola, by completing the square.