Let f ´ (sin x) f ´´ (sin x) > 0 x (0, 2 ) Now consider a function g (x) = f (sin x) + f…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Let f ´ (sin x) < 0 and f ´´ (sin x) > 0 \(\forall \mathrm{x} \in\left(0, \frac{\pi}{2}\right)\)
Now consider a function g (x) = f (sin x) + f (cos x)
The set of critical points of g (x) is
- \(\left\{\frac{\pi}{8}, \frac{\pi}{6}\right\}\)
- \(\left\{\frac{\pi}{8}, \frac{\pi}{6}, \frac{\pi}{3}\right\}\)
- \(\left\{\frac{\pi}{8}, \frac{\pi}{6}, \frac{\pi}{4}\right\}\)
- none of these
Answer
(D) none of these
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The least value of the function (x)= _ 5 / 4 ^ x (35 i n t+4 t) d t in the interval [ 5 4 , 4 3 ] is ...
- If y = A cos nx + B sin nx, then d ^ 2 y dx ^ 2 =
- If f( x )= a ^ a ^ | x | sgn x ; g( x )= a ^ [ a ^ | x | sgn x ] for a > 1 and x ∈ R, where & [ ] denote the…
- The function f(x)= ^ -1 ( x+ x) is a/an :
- Assertion : Shortest distance between | x | + | y | = 2 & x 2 + y 2 = 16 is 4- 2 Reason : Shortest distance…
- If _ x ( x^ 2 -1 x+1 -a x-b )=2 , then find the value of b .
- Consider a function f( x )= ( - 1 - x ) (4 – 3x 2 ) where ‘α’ is a positive parameter Least possible value of…
- Consider the following statements S and R : S : Both sin x and cos x are decreasing functions in the interval…
More Limit, Continuity and Differentiability questions · Browse all practice questions