For every twice differentiable function f: R [-2,2] with ( f (0)) 2 + ( f ′(0)) 2 = 85…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
For every twice differentiable function \(f: \mathbb{R} \rightarrow[-2,2]\)
with (f(0))2 + (f ′(0))2 = 85, which of the following statement(s) is (are) TRUE?
with (f(0))2 + (f ′(0))2 = 85, which of the following statement(s) is (are) TRUE?
- There exist r, s ∈ , where r < s, such that f is
one-one on the open interval (r, s) - There exists x0 ∈(−4, 0) such that |f ′(x0)| ≤ 1
- There exists a ∈ (−4, 4) such that f(a)+f ′′(a) = 0 and f ′(a) ≠ 0
Answer
(D) There exists a ∈ (−4, 4) such that f ( a )+ f ′′ ( a ) = 0 and f ′ ( a ) ≠ 0
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- If G(x)=- 25-x^ 2 then _ x 1 ( G(x)-G(1) x-1 )=
- Let f : R → R , g : R → R and h : R → R be differentiable functions such that f ( x ) = x 3 + 3 x + 2, g ( f…
- Where [ x ] denotes the greatest integer less than or equal to x then _ x 0 f(x) equals
- If f(x)=A ( x 2 )+B, f^ ( 1 2 )= 2 , then constants A and B are
- If f ( x ) is differentiable and strictly increasing function, then the value of is
- Let f be a real-valued function defined on the interval (0, ∞) by f(x)= x+ _ 0 ^ x 1+ t d t Then which of the…
- If y = a ln x + bx 2 + x has its extremum values at x = –1 and x = 2, then
- The derivative of f (tan x) w.r.t. g (sec x) at x = 4 , where f ’(1) = 2 and g ’ ( 2 ) = 4, is
More Limit, Continuity and Differentiability questions · Browse all practice questions