1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Limit/Derivative Question

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data

    http://img159.imageshack.us/img159/8161/64625334ex7.png [Broken]

    2. Relevant equations

    3. The attempt at a solution


    f(a)=x^3 and f(a)=8

    I'm pretty sure that the answer of f(a)=2 is right but is there a better way to show it and I'm also unsure if I answered it fully.
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Apr 25, 2007 #2
    f(a) is not 2. The limit actually refers to the derivaive of the function at the point 2. Therefore, a=2.
  4. Apr 25, 2007 #3
    Okay; a=2

    How do I show this though because if there's a test, the teacher isn't going to give me marks because I didn't show my work.
  5. Apr 25, 2007 #4
    I would write:
    f(a+h) = (2 + h)^3, hence a+h=2+h, hence a=2. Therefore f(x)=x^3. Assume it is correct and use the other part of the equation to confirm the assumption.

    f(a)=8. We use previously found formula -> f(a)=a^3=8. We solve for a.
    a=2 what holds according to the data provided.
  6. Apr 25, 2007 #5


    User Avatar
    Homework Helper

    i guess it is a matter of comparing with the standard formula:
    [tex]\lim_{h\rightarrow 0}\; \frac{f(x+h)-f(x)}{h}[/tex]

    so all I think you need to do is the following:
    [tex]\lim_{h\rightarrow 0}\; \frac{(2+h)^3-8}{h} =
    \lim_{h\rightarrow 0}\; \frac{(2+h)^3-2^3}{h}
    = \left.\lim_{h\rightarrow 0}\; \frac{(x+h)^3-x^3}{h}\right|_{\text{at}\; x=2}
    then you can identify what f(x) and x=a are.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook