If f (x) is a differentiable function and φ (x) is twice differentiable function and α…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
If f (x) is a differentiable function and φ (x) is twice differentiable function and α and β are roots of the equation f (x) = 0 and φ′ (x) = 0 respectively, then which of the following statement is true ? (α < β).
- there exists exactly one root of the equation
φ′ (x). f ′(x) + φ′′(x). f (x) = 0 and (α, β) - there exists at least one root of the equation
φ′ (x). f ′(x) + φ′′(x). f (x) = 0 and (α, β) - there exists odd number of roots of the equation
φ′ (x). f ′(x) + φ′′(x). f (x) = 0 and (α, β) - None of these
Answer
(B) there exists at least one root of the equation φ′ (x). f ′ (x) + φ′′ (x). f (x) = 0 and ( α, β )
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The set of values of 'a' for which the function f(x)=x^ 2 +a x+1 is an increasing function on [1,2] are :
- The interval in which the function x 3 increases less rapidly than 6x 2 + 15x + 5 is :
- The tangent to the curve 5x 2 + y 2 = 1 at ( 1 3 ,- 2 3 ) passes through the point
- Find the fraction which exceeds its n th power by the greatest possible number (n > 1).
- If f (x) = l og |x|, x ≠ 0 then f ′(x) equals
- A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate…
- If α, β are the roots of x 2 – ax + b = 0, then _ x e^ x^ 2 -a x+b -1 x- is
- A function f such that f ´(a) = f ´´ (a) = ... f 2n (a) = 0 and f has a local maximum value b at x = a, if f…
More Limit, Continuity and Differentiability questions · Browse all practice questions