1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivative physics question

  1. Oct 10, 2007 #1
    1. The problem statement, all variables and given/known data
    Each of the limits represent a derivative f'(a). Find f(x) and a.
    1) lim x-> 0 [(6^x) - 1]/x
    2) lim x-> 0 [((4+h)^(-2)) - 0.0625]/h

    2. The attempt at a solution

    i'm not sure what i'm suppose to be solving for, they give us a derivative, or a partial derivative thats not completely solved and they want us to go backward to find the original function and the number that gave us the derivative they have. How do we do this without integrating.
  2. jcsd
  3. Oct 10, 2007 #2
    How about using the definition of a derivative...
  4. Oct 10, 2007 #3
    Okay but i never even thought of that...
    lim x -> 0 [f(a+x)-f(a)]/x = lim x -> 0 [(6^x) - 1]/x

    so does that mean f(a+x) = 6^x, and f(a) = 1

    than to find f(x) you do f(a+x)-f(a) = 6^x - 1

    than a = 6^a = 2 than you take the log of that to find a?
  5. Oct 11, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    You never even thought of that? The problem said each was a derivative? Don't you associate derivatives with limits?

    No, a is not 6^a and certainly not 2 (where did you get the 2 from?). What is 6^0?
    Now what do you think f(x) and a are?

    For the second problem you might want to calculate (1/4)2 as a decimal number.
  6. Oct 11, 2007 #5
    i was being sarcastic, of course that's the first thing i did...

    i think on the bottom of my last post i meant to put

    f(a+x) = 6^x, and f(a) = 1 Therefore, f(x) = 6^x - 1
    if you stuff a in for x, to get f(a), you get it f(a) = 6^x - 1
    Since f(a) = 1
    1 = 6^x -1
    6^x = 2
    do a log to find a

    OR... do i take the limit somewhere in there to find 6^0 = 1 and it'll all make sense...
  7. Oct 11, 2007 #6


    User Avatar
    Science Advisor
    Homework Helper

    What about f(0 + x) = 6^x (suggestive notation... hope that rings a bell)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Derivative physics question
  1. Derivative Question (Replies: 5)

  2. Derivative Question (Replies: 8)

  3. Derivative Question (Replies: 5)

  4. Derivative question (Replies: 1)

  5. Derivate question (Replies: 6)