sample question 13 of msqe 2010

[priyanka p]

let f and g be two functions-------------f'(@) equals   answer was option b 2g'(@).............  sir please explain how we get this answer and which topic these sort of questions of value relate to?   similar type question 23 and 29 of sample problems how v compute them?

[duck]

hi priyanka,

we will do the que using logic and answer  option (b) 2g'(@) ..

As per ques ,  if f(x) and g(x) are differentiable functions  on (0, 1) such that f(0) = 2,
f(1) = 6, g(0) = 0 and g(1) = 2 then , there exists @ such that  f'(@) = any of the four options.

We will consider each option seperately>>

let f(x)=4x+2 and g(x)=2x
these two functions satisfies the given conditions>> f(0) = 2,
f(1) = 6, g(0) = 0 and g(1) = 2.

so , we have found two differentiable functions
but there is no @ for which
for which f'(@) =1/2g'(@)
so, option 1 cannot be the answer

again , we have no @ for which f'(@)=6g'(@)
so, option 3 cannot be the answer


Again, we have no @ for which f'(@)=1/6g'(@)
so, option 4 also cannot be the answer

But , we have @ for which f'(@)=2g'(@)
so, option 2 is the answer.



P.S : f(x)=4x+2     and   g(x)=2x
=> f'(x)=4            and    g'(x)=2
=>f'(x)=2*g'(x)