Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ksandoval

how do i find the critical points of f(x) = (x-2)^5 (x+3)^4?

  • one year ago
  • one year ago

  • This Question is Closed
  1. freewilly922
    Best Response
    You've already chosen the best response.
    Medals 0

    How would you explain a critical point? A minimum/maximum? a zero?

    • one year ago
  2. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm i dont know haha... i know that i need to find the derivative first though.

    • one year ago
  3. freewilly922
    Best Response
    You've already chosen the best response.
    Medals 0

    A critical point of a function of a single real variable, ƒ(x), is a value x0 in the domain of ƒ where either the function is not differentiable or its derivative is 0,

    • one year ago
  4. freewilly922
    Best Response
    You've already chosen the best response.
    Medals 0

    So it sounds like you need to take the derivative, set it to zero and then solve for x.

    • one year ago
  5. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    and i got \[f'(x) = 5(x-2)^4(x+3)^4 + 4(x+3)^3(x-2)^5\]

    • one year ago
  6. ksandoval
    Best Response
    You've already chosen the best response.
    Medals 0

    embarrassing, but i honestly have no idea how to factor that. ha.

    • one year ago
  7. freewilly922
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, the idea is to find an alternative to brute force.

    • one year ago
  8. freewilly922
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, when things look ugly like this, substitute something easy. Like A= x-2 and B=x+3 This gives you \[f'(X) = 5A^4B^4 +4B^3A^5\] This is easy to factor and set to zero. Then once you have solved for when THIS is zero with respect to A and B then resubstitute the A=x-2 and B=x+3 to get you final answer.

    • one year ago
    • Attachments:

See more questions >>>

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.