JEE Main | 2014Set, Relation and FunctionHard
Question
If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈ ]0, 1[
Options
A.f′(c) = g′(c)
B.f′(c) = 2g′(c)
C.2f′(c) = g′(c)
D.2f′(c) = 3g′(c)
Solution
Using, mean value theorem
f′(c) =
= 4
g′(c) =
= 2
so, f′(c) = 2 g′(c)
f′(c) =
= 4g′(c) =
= 2so, f′(c) = 2 g′(c)
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