Originally Posted by

**Educated** I don't think the answer quoted is correct.

When I tried differentiating the equation $\displaystyle h=\dfrac{90.9x-4.55x^2}{10.16+0.4x}$, i didn't get $\displaystyle x^2+50.7x-507.4=0$

And when you put $\displaystyle x^2+50.7x-507.4=0$ into the quadratic formula, you don't get x=8.65, you get x = -13.72 and x = -36.98.

If you recall the quotient rule, $\displaystyle f'(x) = \dfrac{g'(x)h(x) - g(x)h'(x)}{[h(x)]^2}$ you would see that the answer should come out as a fraction, not as a quadratic binomial. Not always, but in this case it should.