A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

For the function f, f'(x)= 2x+1 and f(1)=4. What is the approximation for f(1.2) found by using the line tangent to the graph of f at x=1?

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

    basically you want to approximate f(1.2) without using integration the idea is that at a point, f' is a farely good approximation of the points around it given that the distance is very close. so the approximation would be more and more off once you go too far. if you wanted to apprx/ f(10) for example, it would be far more off than the apprx. of f(1.2)

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

    help me please

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

    anyways, you just use a line tangent to f to apprx. in order to do that, you find the linear equation that is tangent to f at that specific point. in your case, the slope of your tangent line can be found by using f'. and it touches f at (1,4) once you find out your linear equation, you plug in x =1.2 are you good so far ?

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

    how do i find my linear equation?

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

    if you know a slope m and a point (a,b) your linear eqn. is y-b = m(x-a)

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

    so you need to find m, and (a,b)

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

    m can be found using f' (a,b) is given as the point on f

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

    so my equation would be y=2x+1?

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

    2x+1 = m at any given point. what you should remember is that f is the curve and f' is the "slope that is tangent to f at a given x" so at x =0, f has a tangent line with slope 1 x = -1/2, f has a tangent line with slope 0. since you are approximating the next point around (1,4) you plug this in to see what it is equal to. in your case, x=1 so m =2(1) +1 = 3. sometimes you will have an equation of f' like f' = ycos(x) for those, you have to plug in y as well to find m.

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

    okay. i did all that and came up with the answer 4.6..is that correct?

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

    f'(x)= 2x+1 and f(1)=4. What is the approximation for f(1.2) f'(1) = 3 and it goes through (1,4) so the line tangent to f at (1,4) has the linear equation y-4 = 3(x-1) all you have to do is to plug in 1.2 = x, so y=3(.2)+4 = 4.6 there you go.

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

    thank you!

  13. 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.