Question

A point is moving along the graph of a given function such that dx/dt is 2 centimeters per second. Find dy/dt for the given values of x.
y = 9x2 + 5
(a) x = -1
dy/dt =____ cm/sec

(b) x = 0
dy/dt =____cm/sec

(c) x = 3
dy/dt =_____ cm/sec
...?

Answer 1

Y = 9x^2 + 5

Use the change rule:

dy / dt = [dy / dx] * [dx / dt]

dy / dx = 18x

and dx / dt = constant = 2 cm / s

Then dy / dt =  [18 x] * 2 = 2*18x = 36x

(a) x = -1
dy/dt = 36(-1) = - 36 cm/sec

(b) x = 0
dy/dt = 36(0) = 0 cm/sec

(c) x = 3
dy/dt =36(3) =  108 cm/sec