Expert: Ahmed Salami - 11/30/2008

Question
A point moves along the curve y=x^2 + 1 in such a way that when x=4, the x coordinate is increasing at the rate of 5 ft/sec. At what rate is the y-coordinate changing at that time?

A) 80 ft/sec
B) 45 ft/sec
C) 32 ft/sec
D) 85 ft/sec
E) 40 ft/sec

I chose (E) because the second derivative is y=2 and when x=4 it's increasing at a rate of 5 ft/sec, which is 20, then multiplied times 2 is 40.

Answer
Hi Charlese,
Note that in this question we are differentiating with respect to a third variable, time t.
We have that dx/dt = 5ft/sec  when x = 4ft
dy/dt = dy/dx . dx/dt
but
dy/dx = 2x
At x = 4
dy/dx = 2(4) = 8
Therefore,
dy/dt = 8 . 5
     = 40 ft/sec

I'm not sure how you've arrived at your own answer.

Regards