Question

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

(a) Give an expression for the rate of change of voltage with respect to time.
(b) Is the rate of change ever zero? Explain.
(c) What is the maximum value of the rate of change?

Answer 1

1.) dV/dt = -187200πSin(120πt)

2.) No

3.) -187200

Step-by-step explanation:

The voltage, V, in volts, in an electrical outlet is given as a function of time, t, in seconds, by the function V=156cos(120πt)

dV/dt = -187200πSin(120πt)

Since the rate of change above is negative, that is, its maximum is negative. definitely, it will never be equal to zero.

The maximum value of the rate of change will be its amplitude, which is

-187200