Question

The Voltage, V (in volts), in an electrical outlet is given as the function of time, t (in seconds), by the function V(t) = 156cos(120pi *t).

What is the maximum value of the rate of change?

Answer 1

if you want you can re-write \( V(t) = 156cos(120pi *t)\) as \( V(t) = Acos(Bt)\) to simplify matters, and then calculate\(\dfrac{dV}{dt}\) which is the rate of change of V with time

to see if calculus will give you the maximum value of the rate of change, next calculate \(\dfrac{d}{dt} \left(\dfrac{dV}{dt}\right) [= \dfrac{d^2V}{dt^2}]\)

next, set \( \dfrac{d^2V}{dt^2}\) to zero and solve, and you are on your way...