# Thread: Rate of change problem

1. ## Rate of change problem

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

a.) Give an expression for the rate of change of the voltage with respect to time.

b.) What is the maximum value of the rate of change.

2. Originally Posted by VkL
The voltage, V , in volts, is an electrical outlet given as a function of time, t, in seconds, by the function V = 156cos(120[pie]t)

a.) Give an expression for the rate of change of the voltage with respect to time.
The rate of change is given by $V ' (t) = 156 (120\pi t)' [ - \sin (120 \pi t) ] = - 150\cdot 120 \pi \sin (120 \pi t)$

b.) What is the maximum value of the rate of change.
The maximum value of $- 150\cdot 120 \pi \sin (120 \pi t)$ occurs when $\sin (120 \pi t) = -1$ (that is the smallest value that sine takes) and so the max values is $(150)(120 \pi)$. (The reason why we want $\sin (120 \pi t) = -1$ and not $\sin (120 t) = 1$ is because we have a negative sign infront and so if we used $\sin (120 \pi t) = -1$ that would give us $-(150)(120 \pi)$ i.e. the minimum value).