A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

if f(x)= 4x^3-21x^2+36x-4, then the graph of f is decreasing and concave up on the interval...

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

    would you like the choices?

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

    a. (3/2, 2) b. (neg. infinity, 7/4) c. (7/4, infinity) d. (7/4, 2) e. (3/2, 7/4)

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

    A plot is attached

    1 Attachment
  4. mathmate
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Given f(x)= 4x^3-21x^2+36x-4. The graph is decreasing when f'(x)<0. f'(x)=12x^2-42x+36 which factors into f'(x)=6(x-2)(2x-3). This means that f'(x) is negative (f(x) decreasing) between 1.5 and 2, or (1.5,2). For concavity, we look at f"(x)=24x-42=6(4x-7), which means that f(x) is concave up when x>7/4, or (7/4,+inf) Therefore f(x) is increasing and concave up between 7/4 and 2, or (7/4,2)

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

    ah thank youu!!

  6. 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.