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I Need help with concept based questions

  1. Sep 10, 2016 #1
    • Member warned that homework questions must go in the Homework sections
    Let f(x) and g(x) be twice differentiable functions on [0,2] satisfying f"(x)=g"(x), f'(1)=4, g'(1)=6,f(2)=3 and g(2)=9.Then what is f(x)-g(x) at x=4 equal to?

    I honestly have no idea how to do it.Please help.
     
  2. jcsd
  3. Sep 10, 2016 #2
    I tried to do it myself and I got -6. This is actually a prev year question so when I checked online the answer was published as 2.
     
  4. Sep 10, 2016 #3

    micromass

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    The question makes no sense. You say the domain is ##[0,2]## but then ask the value at ##4##?
     
  5. Sep 10, 2016 #4
    No. The value of f(x)-g(x) if x=4.
    So value of f(4)-g(4).
     
  6. Sep 10, 2016 #5

    micromass

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    ##f(4)## makes no sense if the domain is ##[0,2]##.
     
  7. Sep 10, 2016 #6

    Math_QED

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    This belongs in the homework section.

    Also, you cannot evaluate the function at x = 4. However, I assume that's some kind of typo.

    Start by integrating ##f(x) = g(x)## twice.
    What do you know? Keep in mind: ##f' = g' \Rightarrow f = g + c##
     
  8. Sep 10, 2016 #7
    So, f"(x)=g"(x)
    Integrating, f'(x)=g'(x)+c ===> (A)
    f(x)=g(x)+cx+d =====(B)
    Since f'(1)=4,
    4=6+c (from A)
    c=-2
    Substituting this in B,
    f(x)=g(x)+-2x+d
    when x=2
    f(2)=g(2)+-2(2)+d
    3=9+-4+d
    d=-2
    Now using B,
    f(x)=g(x)+-2(x)+-2
    f(x)-g(x)=-2(x)-2
    when x=4,
    f(4)-g(4)= -8-2=-10?

    what did I do wrong?Also sorry about the wrong section. I just joined 3 days ago so I thought science questions go to one section and math questions go to another section.
     
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