A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

consider f(x)=x^2+1 find f'(1) using the definition of derivative

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The definition of a derivative is f(x+h)-f(x) all over h.

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the "definition" being: f(x+h) - f(x) lim ----------- h right?

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And yes there is a limit, forgot that part. lim as h approaches 0.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes that is right. is get confused when i see h^2 as part of the solution. is the x+h always squared?

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What do you mean always squared?

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (1+h)^2 + 1 - (1^2 + 1)//h h^2 +2h +1 +1 -1 -1//h h^2 +2h // h h(h+2)//h h+2 is what I get if I did it right....

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i mean party of his answr is 2+2h+h^2-2/h 2h+h^2/5 h(2+h)/5 2+5=2 yes the limit is zero

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    as h->0; h+2 = 2 f'(x) = 2x; f'(1) = 2

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that aint no 5....

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the squared question is asked is ist the (1-h)^2. will i always sqaure the X+h?

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i mean h. i always seem to hit 5

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You will only square the x+h if your function has a 2nd degree in it somewhere.

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok.... f(x) = x^2 +1 whatever value x is ... is the value you use for x. :)

  14. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(1+h) is the value you use and f(1) is the other...

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so if its not to a power, you will not square it. just multiply normally?

  16. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ....youve confused me

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What you are basically doing is plugging in (x+h) into the function for x then subtracting the function itself and dividing by h. All while calculating the limit.

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and x = 1 in this instance :)

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes to see if i understand if it was just +1, not x^2 +, would you not square it?

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(1+h) - f(1) // h [(1+h)^2 +1] - [1^2 +1] // h

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So if you have f(x)=x+1 there is no squaring involved.

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that is something i always wanted to know thank you. i will be posting a couple more questions of confusion

  23. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    [h^2 +2h +1 +1] - [2] //h h^2 + 2h +2 - 2 //h h^2 + 2h // h h(h+2)//h lim{h->0} h+2 = 0+2 = 2

  24. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f'(x) = 2x f'(1) = 2(1) = 2 same answers :)

  25. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.