Need help with concept based questions

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Discussion Overview

The discussion centers around a mathematical problem involving two twice differentiable functions, f(x) and g(x), defined on the interval [0,2]. Participants are attempting to determine the value of f(x) - g(x) at x = 4, despite the stated domain limitations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to approach the problem and requests help.
  • Another participant claims to have calculated f(4) - g(4) as -6 but found an online answer of 2, indicating a discrepancy.
  • Several participants point out that the question is problematic because it asks for a value outside the given domain of [0,2].
  • One participant suggests that the question may contain a typo and proposes starting by integrating the functions based on the information provided.
  • A participant derives relationships between f(x) and g(x) through integration, leading to an expression for f(x) - g(x) and calculates it at x = 4, arriving at -10, but questions their own reasoning.
  • Another participant apologizes for posting in the wrong section, indicating they are new to the forum.

Areas of Agreement / Disagreement

Participants generally agree that the question is flawed due to the domain issue, but there is disagreement regarding the calculations and interpretations of the functions involved. The discussion remains unresolved regarding the correct approach to the problem.

Contextual Notes

There are limitations related to the domain of the functions, as participants highlight that evaluating f(4) and g(4) is not valid given the stated domain of [0,2].

Deebu R
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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.
 
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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.
 
The question makes no sense. You say the domain is ##[0,2]## but then ask the value at ##4##?
 
micromass said:
The question makes no sense. You say the domain is ##[0,2]## but then ask the value at ##4##?
No. The value of f(x)-g(x) if x=4.
So value of f(4)-g(4).
 
##f(4)## makes no sense if the domain is ##[0,2]##.
 
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##
 
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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