1. ## Calculus Question

A small plane is 34 miles east of an airport runway (at the origin) and starts to descend to the airport according to the formula h = -.00034x^3 +.0173 x^2 +.098x where h is the height of the plane and x is the distance of the plane from the runway. How far from the runway (to the nearest mile) would the plane be descending at the greatest rate?

I started by taking the second derivative, and am not even sure if that is right, any help is appreciated.

2. Originally Posted by CalcGeek31
A small plane is 34 miles east of an airport runway (at the origin) and starts to descend to the airport according to the formula h = -.00034x^3 +.0173 x^2 +.098x where h is the height of the plane and x is the distance of the plane from the runway. How far from the runway (to the nearest mile) would the plane be descending at the greatest rate?

I started by taking the second derivative, and am not even sure if that is right, any help is appreciated.
You want the greatest negative rate - in other words, the LEAST rate.

So you want to find the minimum rate.

Take the second derivative and set it equal to 0 to find the maximum and minimum rates.

Suppose you get a minimum rate at $x = a$. Take the third derivative and check it's sign at $x = a$. If $h'''(a) > 0$ you have a minimum.

3. then would i plug that value into the original equation?