Let f : R R be a function such that and f ′ (0) = 3 . Then

Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability

Let f : R R be a function such that
and f ′ (0) = 3 . Then

1. f (x) is a quadratic function
2. f (x) is continuous but not differentiable
3. f (x) is differentiable in R
4. f (x) is bounded in R

Answer

(C) f (x) is differentiable in R

Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.

Related practice questions

• Let f : R → R be given by f(x)= array ll x^ 5 +5 x^ 4 +10 x^ 3 +10 x^ 2 +3 x+1, & x Then which of the…
• Consider the functions defined implicitly by the equation y 3 – 3 y + x = 0 on various intervals in the real…
• Let f(x)=x^ n , n ~W . The number of values of n for which f^ (p+q)=f^ (p)+f^ (q) is valid for all +ve p & q…
• Let f (x) = a + b |x| + c |x| 4 , where a, b and c are real constants. Then f (x) is differentiable at x = 0…
• Which of the following functions are continuous on (0, π ) ?
• _ h 0 2 [ 3 ( 6 +h )- ( 6 +h ) ] 3 h( 3 h- h) is equal to
• _ n 1 n (1+e^ 1 / n +e^ 2 / n + +e^ n-1 n ) is equal to
• The function f(x)= ( +x) (e+x) is

More Limit, Continuity and Differentiability questions · Browse all practice questions