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Math Help - Rate of change problem

  1. #1
    VkL
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    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.
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    Quote Originally Posted by VkL View Post
    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).
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