Set, Relation and FunctionHard
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 w = α + iβ, where β ≠ 0 and z ≠ 1, satisfies the condition that is purely real, then the s...Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total n...If A denotes the area between the curve 2{y} = [x] + 1 for 0 ≤ y 2 - x ≤ 0, then A is less than or equal to ...A mapping is selected at random from all the mapping of set S = {1, 2, 3, .... , n} to itself such that the probability ...If are two unit vectors such that and be a vector such that then is equal to (where [.] represents greatest integer func...