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Math Help - Using deritative to calc irc

  1. #1
    Newbie crazydaizy78's Avatar
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    Using deritative to calc irc

    Use the deritative to calculate the instanteous rate of change of the given input value. (You can eliminate the h algebraically.

    13. s(t)=16r^2+64 where t=2

    I haven't a clue where to start...limits are foreign to me. Please help if you can.
    Thanks a million!!
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  2. #2
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    Quote Originally Posted by crazydaizy78 View Post
    Use the deritative to calculate the instanteous rate of change of the given input value. (You can eliminate the h algebraically.

    13. s(t)=16t^2+64 where t=2 Mr F edit in red.

    I haven't a clue where to start...limits are foreign to me. Please help if you can.
    Thanks a million!!
    You've got to overcome your xenophobia!

    First find \frac{s(t+h) - s(t)}{h}:


    1. s(t + h) = 16(t + h)^2 + 64 = 16(t^2 + 2th + h^2) + 64= 16t^2 + 32 th + 16h^2 + 64.



    2. s(t + h) - s(t) = 16t^2 + 32 th + 16h^2 - (16t^2 + 64)

    = 16t^2 + 32 th + 16h^2 - 16t^2 - 64 = 32 th + 16h^2.



    3. \frac{s(t+h) - s(t)}{h} = \frac{32 th + 16h^2}{h} = 32t + 16h.


    Now let h --> 0: \lim_{h \rightarrow 0}\frac{s(t+h) - s(t)}{h} = 32t + 16(0) = 32t.


    Now sub t = 2. You get 64.
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