Let f(x)=x ^ -1 (- |x|), x [- 2 , 2 ] , then which of the following is true?
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Let \(f(x)=x \cos ^{-1}(-\sin |x|), x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), then which of the following is true?
- \(f^{\prime}(0)=-\frac{\pi}{2}\)
- f' is decreasing in \(\left(-\frac{\pi}{2}, 0\right)\) and increasing in \(\left(0, \frac{\pi}{2}\right)\)
- f is not differentiable at x = 0
- f' is increasing in \(\left(-\frac{\pi}{2}, 0\right)\) and decreasing in \(\left(0, \frac{\pi}{2}\right)\)
Answer
(C) f is not differentiable at x = 0
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Derivative of x 6 + 6 x with respect to x is
- If y= _ u(x) ^ v(x) f(t) d t let us define d y d x in a different manner as d y d x =v^ (x) f^ 2 (v(x))-u^…
- The equation of the tangent to the curve (1 + x 2 ) y = 2 –x, where it crosses the x-axis, is
- Differentiate the following function ^ -1 [x 1-x + x 1-x^ 2 ]
- If f(x) = _ x^ 2 ^ x^ 2 +1 e^ -t^ 2 d t_ 1 then the function f(x) decreases in
- _ x 3 ([x-3]+[3-x]-x), where [.] denotes the greatest integer function, is equal to
- If the function f(x)= array ll a| -x|+1, & x 5 b|x- |+3, & x>5 array . is continuous at x = 5, then value of…
- The point in the interval [0, 2π], where f (x) = e x sin x has maximum slope, is
More Limit, Continuity and Differentiability questions · Browse all practice questions