Results 1 to 3 of 3

Thread: help finding info about a function without knowing the actual function??? i

  1. #1

    Red face help finding info about a function without knowing the actual function? (AP Calc AB)

    given that f is continuous on [-2,5] and...
    f(-2)=10

    f(5)=6

    f'(x) is positive on (-2. 1) and (3,5); negative on (1,3); 0 at x=1 and undefined at x=3

    f''(x) is positive on (3, 5), negative on (-2, 1) and (1,3); 0 at x=0. and undefined at x=3

    a)find intervals where f is increasing or decreasing
    b) find where f has absolute extrema
    c) find where f has points of inflection
    d) find intervals where f is concave up and concave down



    i tried working through it & got..


    a) I: [2,-1] and (3,5] D: [1,3) (not sure about use of brackets vs parenthesis with the 3 since it's undefined??)

    b) x=1 max, x=3 min based on my rough sketch of the graph..

    c) IP at x=3? can this occur at an undefined???

    d)cc up on (3, 5) cc down on (-2, 3).. but should the interval be more precise? is (3, 5) concave up??

    please correct/guide me.. I really want to understand this for the AP exam!!!
    Last edited by gallentlyspeaking; 12-01-2016 at 11:43 PM.

  2. #2
    Elite Member stapel's Avatar
    Join Date
    Feb 2004
    Posts
    15,909

    Cool

    Quote Originally Posted by gallentlyspeaking View Post
    given that f is continuous on [-2,5] and...
    f(-2)=10

    f(5)=6

    f'(x) is positive on (-2. 1) and (3,5); negative on (1,3); 0 at x=1 and undefined at x=3

    f''(x) is positive on (3, 5), negative on (-2, 1) and (1,3); 0 at x=0. and undefined at x=3

    a)find intervals where f is increasing or decreasing
    b) find where f has absolute extrema
    c) find where f has points of inflection
    d) find intervals where f is concave up and concave down

    i tried working through it & got..

    a) I: [2,-1] and (3,5] D: [1,3) (not sure about use of brackets vs parenthesis with the 3 since it's undefined??)
    Isn't the function increasing only where the derivative is positive, not just non-negative? So should points outside the intervals of positivity be included, or excluded? Same question for the interval of negativity.

    Quote Originally Posted by gallentlyspeaking View Post
    b) x=1 max, x=3 min based on my rough sketch of the graph..
    I agree.

    Quote Originally Posted by gallentlyspeaking View Post
    c) IP at x=3? can this occur at an undefined???
    How does your book define "inflection point"?

    Quote Originally Posted by gallentlyspeaking View Post
    d)cc up on (3, 5) cc down on (-2, 3).. but should the interval be more precise? is (3, 5) concave up??
    The point where the second derivative is zero: is that included in the intervals of concavity? According to the definition here, no. What is your book's definition? Otherwise, I agree with your intervals.

  3. #3
    Senior Member
    Join Date
    Dec 2014
    Posts
    2,185
    Quote Originally Posted by gallentlyspeaking View Post
    given that f is continuous on [-2,5] and...
    f(-2)=10

    f(5)=6

    f'(x) is positive on (-2. 1) and (3,5); negative on (1,3); 0 at x=1 and undefined at x=3

    f''(x) is positive on (3, 5), negative on (-2, 1) and (1,3); 0 at x=0. and undefined at x=3

    a)find intervals where f is increasing or decreasing
    b) find where f has absolute extrema
    c) find where f has points of inflection
    d) find intervals where f is concave up and concave down



    i tried working through it & got..


    a) I: [2,-1] and (3,5] D: [1,3) (not sure about use of brackets vs parenthesis with the 3 since it's undefined??)

    b) x=1 max, x=3 min based on my rough sketch of the graph..

    c) IP at x=3? can this occur at an undefined???

    d)cc up on (3, 5) cc down on (-2, 3).. but should the interval be more precise? is (3, 5) concave up??

    please correct/guide me.. I really want to understand this for the AP exam!!!
    Please show us your graph.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •