Question

If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units per second, and g equals 5 and is rising at a rate of 6 units per second, then fg equals ___ and is rising at a rate of ___ units per second.

Answer 1

Your givens are f(2) = 2 , f'(2) = 3), g(2) = 5, g'(2) = 6
If h(t) = f(t)*g(t), then h(2) = f(2) * g(2) = 2 * 5 = 10
The trickier one is h'(t). Use the product rule.
h'(t) = f(t)*g'(t) + f'(t)*g(t)
So,
h'(2) = f(2) * g'(2) + f'(2) * g(2) = you can finish it off.

Answer 2

@BangkokGarrett fg=10 and is rising at 8 units per second?

Answer 3

h'(2) = f(2) * g'(2) + f'(2) * g(2)
= 2 * 6 + 3 * 5
= 12 + 15 = 27
rising at 27 units per second

Answer 4

haha oops did it totally wrong, got it thanks! #lifesaverstatus