A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 3 years ago

Can someone explain problems 2B-7 a & b. I've reviewed the answer and it doesn't make sense to me. I'm missing a concept here. http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-2-applications-of-differentiation/part-a-approximation-and-curve-sketching/problem-set-3/MIT18_01SC_pset2prb.pdf

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

    If f(x) is increasing at a given point, then the slope at that point has two forms it could be in. Either y and x are both positive, or y and x are both negative. If y and x are both negative, then the negatives on the top and bottom of the fraction cancel, and the slope is still positive. Therefore, when f(x) is increasing, the slope is always positive (or zero, as you will see shortly, hopefully). The derivative gives us a method to calculate the slope at a given point, hence, if f(x) is increasing, the derivative at that given point is positive. Since the limit of a continuous function is the same as the derivative at a given point, you can use the limit to prove this. For part b, x to the third power has an inflection point, a point were the function is increasing, and then for one instance goes horizontal and has slope of zero. It's just one point. Then it increases again. The function is said to be increasing at this inflection point because it does not decrease. It simply goes from increasing, to horizontal for one instantaneous point, and then increasing again.

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

    Thank you for your explanation. When I revisited the problem with your explanation, it help connected the dots.

  3. 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...


  • 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.