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)
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let p(x) be a function defined on R such that p′(x) = p′(1 - x), for all x ∈ [0, 1], p(0) = 1 and p(1)...The range of k for which the inequality k cos2x - k cos x + 1 ≥ 0 ∀ x ∈ R, is -...Let a differentiable function f(x) be such that 3|f(x) - f(y)| ≤ 2|x - y| ∀ x, y ∈ R and f′(x) &...The number of relations, defined on the set $\{ a,b,c,d\}$, which are both reflexive and symmetric, is equal to:...Let f(x) be a differentiable function on interval (0, ∞) such that f(1) = and then f(2) has value equal to...