1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus problem.

  1. Oct 30, 2004 #1
    first problem : Let A and B be postitive numbers. SHow that not both of the numbers a(1-b) and b(1-a) can be greater than 1/4.

    second problem : Find a function f such that fprime(-1) = 1/2,fprime(0) = 0
    and f doubleprime (x) >0 for all x, or prove that sucha function cannot exist.

    thanks in advance!
  2. jcsd
  3. Oct 30, 2004 #2


    User Avatar
    Homework Helper



    plotting this on the ab plane gives the boundary of the regions where a(1-b)<1/4 and where a(1-b)>1/4. Starting with an (a,b) on the curve, adding a little to a will obviously give a(1-b)>1/4, and subtracting a little from a will give a(1-b)<1/4, so the region we want is above the curve. swapping a and b to get the second inequality is the same as reflecting this region over the line a=b, so to show these regions do not overlap, all you have to do is show the hyperbola does not cross the line a=b.

    the second question is easier. if f''(x) is always positive, f'(x) is always increasing as you move left to right.
    Last edited: Oct 30, 2004
  4. Oct 30, 2004 #3


    User Avatar
    Science Advisor
    Homework Helper

    For the second one.If f''(x)>0 for all x, then the graph of the function 'bends upwards', it is convex. That means f' is always increasing.
    (I assumed f''(x)>0 for all x, implies f''(x) exists for anyl real number x).
  5. Oct 30, 2004 #4
    thanks for the quick response guys!
  6. Oct 30, 2004 #5
    so showing that a= 1/(4-4b) a= (4b-1)/4b gotten from a(1-b) =1/4, b(1-a)=1/4
    only intercept once shows that there is no where that this is true
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Calculus problem.
  1. Calculus problem (Replies: 5)

  2. A problem on calculus (Replies: 1)