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!

Linear approximations

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    explain in terms of linear approximations why the approximation is reasonable.

    2. Relevant equations
    L(x)=f(a) + f'(a)(x-a)

    3. The attempt at a solution
    given 1.01^6, f(x)=x^6, so f'(x)=6x^5
    plugging in x=1, f'(1)=6

    Is that the right equation?
    Because in class the equation was
    which is the correct answer. But why is y1=1 and not 6??? Can anyone catch that?
  2. jcsd
  3. Oct 3, 2007 #2

    Where m is your slope and the point given is (x1,y1), since f(1)=1 your point is (1,1)
    f'(1)=6=m so...

  4. Oct 3, 2007 #3
    They didn't give me P(1,1) though
    I arbitrarily picked x=1 to solve the original f'(x) equation.
  5. Oct 3, 2007 #4
    Isn't my point (1,6)
    I plugged in x=1 and got f'(x)=6
  6. Oct 3, 2007 #5
    Yes f'(1)=6 but that doesn't mean when x=1 f(x)=6 necessarily. The point of a function f(x) at x is (x,f(x)). What does the derivative tell us about f(x)?
  7. Oct 3, 2007 #6
    So f'(x)=6, but f(x)=1 so f(x) is the value I should put in for y in (x1,y1)?
  8. Oct 4, 2007 #7


    User Avatar
    Staff Emeritus
    Science Advisor

    I hope it was NOT "arbitrary". The fact that 1 is very close to 1.01 should have guided you!

    f(x) is NOT "1", the function you are looking at is f(x)= x6. What is f(1)= (1)6?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear approximations
  1. Linear approximation (Replies: 4)

  2. Linear approximation (Replies: 1)

  3. Linear Approximation (Replies: 4)

  4. Linear Approximations (Replies: 3)