Question

The seat of a ride at a theme park is conveyed along the curve y = 4 arctan(2x) by a hidden apparatus
that moves the seat in the horizontal direction at a rate of 1.5 feet per second. At what rate does
the seat move in the vertical direction when x = 0? when x = 5? (In the plane, assume x and y are
measured in feet.)

Answer 1

I know I have to take the derivative. But I have no idea what the equation is.

Answer 2

I made a picture, but it's not helpful

Answer 3

i think they have just given it to you to use

Answer 4

oh woops. this is the wrong problem.

Answer 5

But just to make sure, I took the derivative.

Answer 6

i.e. \(x\) is the vertical direction, \(y\) is the horizontal direction and you are told \(x'=1.5\)

Answer 7

\[y'=\frac{ 2x' }{ 1+4x^{2} }\]

Answer 8

Right, then I plugged in x'=1.5 and x=0 and 5

Answer 9

what happened to the 4?

Answer 10

woops 8x'

Answer 11

I did it right, I just wrote it here wrong.

Answer 12

for x=0, I got 12 and for x=5, I got 0.12

Answer 13

ft/s?