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duck on
URL: http://discussion-forum.276.s1.nabble.com/sample-question-13-of-msqe-2010-tp4888921p4902728.html
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)
:)