Set, Relation and FunctionEasy
Question
f(x) and g(x) are two differentiable functions on [0, 2] such that f″(x) - g″(x) = 0 f′(1) = 2g′(1) = 4f(2) = 3g(2) = 9 then f(x) - g(x) at x = 3/2 is
Options
A.0
B.2
C.10
D.5
Solution
∵ f″(x) - g″(x) = 0
Integrating, f′(x) - g′(x) = c ⇒ f′(1) - g′(1) = c ⇒ 4 - 2 = c ⇒ c = 2
∴ f′(x) - g′(x) = 2 ; Integrating, f(x) - g(x) = 2x + C1
⇒ f(2) - g(2) = 4 + c1 ⇒ 9 - 3 = 4 + c1 ⇒ c1 = 2 ∴ f(x) - g(x) = 2x + 2
At x = 3/2, f(x) - g(x) = 3 + 2 = 5
Integrating, f′(x) - g′(x) = c ⇒ f′(1) - g′(1) = c ⇒ 4 - 2 = c ⇒ c = 2
∴ f′(x) - g′(x) = 2 ; Integrating, f(x) - g(x) = 2x + C1
⇒ f(2) - g(2) = 4 + c1 ⇒ 9 - 3 = 4 + c1 ⇒ c1 = 2 ∴ f(x) - g(x) = 2x + 2
At x = 3/2, f(x) - g(x) = 3 + 2 = 5
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then...Consider any set of 201 observations x1, x2,...., x200, x201. It is given that 1 2 200 201. Then the mean deviation of t...Let X = {1, 2, 3, 4, 5}. The number of differentordered pairs (Y, Z) that can be formed suchthat and is empty, is :...The set {x : x ∈ N, x is prime and 3 < x < 5} is-...Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is...