Differentiability: JEE Questions & Solutions

Let α,β∈ℝ be such that the function f(x)= 2α(x²-2)+2β x, x<1 (α+3)x+(α-β), x≥1 is differentiable at all x∈ℝ. Then 34(α+β) is equal to

Let the function, f(x) = -3ax² - 2, x < 1 a² + bx, x ≥ 1 Be differentiable for all x ∈ ℝ, where a > 1, b ∈ ℝ. If the area of the region…

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) = (x² - 1)|x² - ax + 2| + cos|x| be not differentiable at the two points x = α = 2 and x = β. Then the distance of…

Let m and n be the number of points at which the function f(x) = max { x, x³, x⁵, …, x²¹ } is not differentiable and not continuous,…

Consider the function f: (0,2) → R defined by f(x) = x/2 + 2/x, and the function g(x) by min{f(t)} for 0 < t ≤ x, 0 < x ≤ 1 and g(x) = 3/2…

Let g: ℝ → ℝ be a non-constant twice differentiable function such that g'(1/2) = g'(3/2). If a real-valued function f is defined as f(x) =…

If the function f(x) = 1/|x|, |x| ≥ 2 ax² + 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)= x²+3x+a, x≤ 1 bx+2, x>1 is differentiable on ℝ. Then, the value of…

Let f(x) = |2x² + 5|x| - 3|, x ∈ ℝ. If m and n denote the number of points where f is not continuous and not differentiable respectively,…

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

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…