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Math Help - First Principles Question

  1. #1
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    First Principles Question

    Hello all

    I am taking an introductory calculus course at the high school level currently and had a question about first principles

    basically when one finds the derivative dy/dx based on first principles, what does the answer represent??

    For example, the function f(t) = -4.9t^2 + 16t + 1

    when you find the derivative of this based on first principles, you get

    -9.8t + 16

    what can i do with the -9.8t + 16, can i use it to find instant rate of change at any value of t or no?

    thanks
    Last edited by kamkal; October 4th 2008 at 09:47 PM.
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  2. #2
    Member Nacho's Avatar
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    the derivative is the slop of the straight line of the curve. We suppose that in axis X is time and in axis Y is position, te slop has unit of velocity.

    In your example -9.8t+16, is the slop in any instant of time, I mean, if you want find the straight line of the curve equation in t=2s, only you subtitute. Then in t=2s our original function we give a position, now you have a point and the slope, whit this you can find the straight line of the curve equation in t=2s

    P.D: if you understan spanish I can explain this better
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  3. #3
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    Quote Originally Posted by Nacho View Post
    the derivative is the slop of the straight line of the curve. We suppose that in axis X is time and in axis Y is position, te slop has unit of velocity.

    In your example -9.8t+16, is the slop in any instant of time, I mean, if you want find the straight line of the curve equation in t=2s, only you subtitute. Then in t=2s our original function we give a position, now you have a point and the slope, whit this you can find the straight line of the curve equation in t=2s

    P.D: if you understan spanish I can explain this better
    no spanish

    but i think i get what you are saying, this -9.8t+16 is the equation to find the slope of the tangent line which is the rate of change and in this case velocity.

    thanks dude
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