JEE Main | 2014Set, Relation and FunctionMedium
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 A = {2, 3, 4, 5} and let R = {(2, 2), (3, 3), (4, 4), (5, 5), (2, 3), (3, 2), (3, 5), (5, 3)} be a relation on A. Th...A function f(x) satisfies the relation f(x + y) = f(x) + f(y) + xy (x + y) ∀, x, y, ∈ R. If f′(0) = - ...The Range of the fucntion y = is : -...Let R be a relation on the set N of natural numbers defined by nRm ⇔ n is a factor of m (i.e. n | m). Then R is -...For real x, let f (x) = x3 + 5x + 1, then...