NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice

If f x = a + c o s - 1 x + b : x ≥ 1 - x : x < 1 is differentiable at x = 1 , then the value of b - a is equal to

Options

A0
B1
C- 1
Dπ 2

Correct answer

D. π 2

Step-by-step solution

Since, f ( x ) is differentiable, it must be continuous at x = 1 ∴ f 1 - = f 1 + = f 1 - 1 = a + c o s - 1 1 + b ... 1 f ' x = − 1 1 − x + b 2 : x ≥ 1 − 1 : x < 1 Now, for f x to be differentiable at x = 1 f ′ 1 − = f ′ 1 + - 1 1 - 1 + b 2 = - 1 ⇒ 1 - 1 + b 2 = 1 ⇒ b = - 1 ... 2 From equation 1 & 2 - 1 = a + π 2 ⇒ a = - π 2 - 1

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let R denote the set of all real numbers. Let f : R R be an arbitrary function and let g : R R be the function defined by g(x) = x f(x) , for all x R . Then which of the following 2026 Consider the function f : (- 2 , 2 ) (- , ) defined by f(x) = (|x| + |x - 1|) x + [x x] , where [x x] is the greatest integer less than or equal to x x . Let be the total number of 2026 For a real number , let [ ] denote the greatest integer less than or equal to . For a finite set S , let |S| denote the number of elements in the set S . Consider the functions f : 2026 For the function f(x) = e^ |x| - |x| , x R , consider the following statements: Statement I: f is differentiable for all x R . Statement II: f is increasing in (- , - 2 ) . In the 2026 Let f(x) = cases 1 3 , & x /2 b(1- x) ( -2x)^2 , & x > /2 cases . If f is continuous at x= /2 , then the value of ₀^ 3b-6 |x^2+2x-3| ,dx is: 2026 Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g f is discontinuous, is __________. 2026 Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x 0 cases and g(x)=f(|x|)+|f(x)| . If the number of points where g is not continuous and is not differentiable are and respectively, then 2026 The number of points, at which the function f(x) = 6x, 2 + 3x^2 + |x - 1| | |x^2 - 1 4 | | , x (- , ) , is not differentiable, is _____. 2026 Full Continuity and Differentiability list All NTA Abhyas JEE Main PYQs