Let f , g : [–1, 2] → R be continuous functions which are twice differentiable on the…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f, g : [–1, 2] → R be continuous functions which are twice differentiable on the interval (–1, 2). Let the values of f and g at the points –1, 0 and 2 be as given in the following table.
\[\begin{array}{|c|c|c|c|} \hline & x=-1 & x=0 & x=2 \\ \hline f(x) & 3 & 6 & 0 \\ \hline g(x) & 0 & 1 & -1 \\ \hline \end{array}\]
In each of the intervals (–1, 0) and (0, 2), the function
(f – 3g)′′ never vanishes. Then the correct statement(s) is(are).
\[\begin{array}{|c|c|c|c|} \hline & x=-1 & x=0 & x=2 \\ \hline f(x) & 3 & 6 & 0 \\ \hline g(x) & 0 & 1 & -1 \\ \hline \end{array}\]
In each of the intervals (–1, 0) and (0, 2), the function
(f – 3g)′′ never vanishes. Then the correct statement(s) is(are).
- f
(–1, 0) - f
- f
- f
Answer
(A) f ′ ( x ) – 3 g ′ ( x ) = 0 has exactly three solutions in (–1, 0) ∪ (0, 2)
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- People living at Mars, instead of the usual definition of derivative D f(x), define a new kind of derivative…
- If y = a ln x + bx 2 + x has its extremum values at x = –1 and x = 2, then
- Suppose the function f(x) – f(2x) has the derivative 5 at x = 1 and derivative 7 at x = 2 . The derivative of…
- Let h ( x ) = f ( x ) – ( f ( x )) 2 + ( f ( x )) 3 for every real number x , Then
- The function f ( x ) = 1 + |sin x | is
- If f (x) = array ll x (3 e^ 1 / x +4 ) 2-e^ 1 / x , & x 0 0 & , x=0 array . , then f (x) is
- The number of points in (–∞, ∞), for which x 2 – x sin x – cos x = 0, is
- If y = ( ax + b cx + d ), then 2 dy dx ~d ^ 3 y dx ^ 3 is equal to
More Limit, Continuity and Differentiability questions · Browse all practice questions