For the function f(x)=x 1 x , x 1
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
For the function \(f(x)=x \cos \frac{1}{x}, x \geq 1\)
- for at least one x in the interval [1, ∞),
f(x + 2) – f (x) < 2 
- for all x in the interval [1, ∞), f (x + 2) – f (x) > 2
- f ′(x) is strictly decreasing in the interval [1, ∞)
Answer
(D) f ′ ( x ) is strictly decreasing in the interval [1, ∞ )
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The function f(x)= array ll |x-3| & , x 1 x^ 2 4 - 3 x 2 + 13 4 & , x<1 array . .
- _ h 0 (a+3 h)-3 (a+2 h)+3 (a+h)- a h^ 3 is
- AP is a diameter of a unit circle with centre at O. Let AC be an arc of this circle, which subtends angle θ…
- If f (a) = 2, f ‘ (a) = 1, g (a) = –1, g ’ (a) = 2, then _ x a g( x ) f( a )-g( a ) f( x ) x - a is equal to
- Let p ( x ) = a 0 + a 1 x 2 + a 2 x 4 + - - - - - a n x 2 n be a polynomial in a real variable x with 0 a 0 a…
- Consider two functions f (x) = _ n ( x n )^ n and g(x) = –x 4b where b = _ x ( x^ 2 +x+1 - x^ 2 +1 ) Then…
- Let [x] denotes the greatest integer less than or equal to x. If f (x) = [x sin π x], then f (x) is
- Given that for each a ∈ (0, 1), _ h 0^ + _ h ^ 1-h t^ -a (1-t)^ a-1 d t exists. Let this limit be g ( a ). In…
More Limit, Continuity and Differentiability questions · Browse all practice questions