Differentiability: JEE Questions & Solutions

Let, R be such that the function f(x)= cases 2 (x^2-2)+2 x, & x<1 ( +3)x+( -), & x 1 cases is differentiable at all x R. Then 34( +) is…

Let the function, f(x) = cases -3ax^2 - 2, & x < 1 a^2 + bx, & x 1 cases Be differentiable for all x R, where a 1, b R. If the area of the…

Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x) = [x] + |x…

Let the function f(x) = (x^2 - 1)|x^2 - ax + 2| + |x| be not differentiable at the two points x = = 2 and x =. Then the distance of the…

Let m and n be the number of points at which the function f(x) = x, x^3, x^5,, x^21 is not differentiable and not continuous, respectively.…

Consider the function f: (0,2) → R defined by f(x) = x^2 + 2x, and the function g(x) by f(t) for 0 < t x, 0 < x 1 and g(x) = ( 32 + x) for…

Let g: R R be a non-constant twice differentiable function such that g' ( 12) = g' ( 32). If a real-valued function f is defined as f(x) =…

If the function f(x) = 1|x|, |x| 2 ax^2 + 2b, |x| < 2. is differentiable on R, then 48(a + b) is equal to:

Let a and b be real constants such that the function f defined by f(x)= casesx^2+3x+a, & x 1 bx+2, & x1 cases is differentiable on R. Then,…

If the function f(x) = cases 1|x|, & |x| 2 ax^2 + 2b, & |x| < 2 cases is differentiable on R, then 48(a + b) is equal to:

Let f(x) = |2x^2 + 5||x| - 3, x R. If m and n denote the number of points where f is not continuous and not differentiable respectively,…

If the function f(x) = 1|x|, |x| 2 ax^2 + 2b, |x| < 2. is differentiable on R, then 48(a + b) is equal to:

Let a Z and [t] be the greatest integer t. Then the number of points, where the function f(x) = [a + 13 x], x (0,) is not differentiable,…

Let f(x) be defined as: f(x) = x x, -2 < x < 0, and f(x) = (x - 1) x, 0 x < 2. If m and n are the number of points in (-2, 2) where y =…