The number of points at which the function $f \left(x\right)=max \left\{a-x, a+x, b\right\}, -\infty, 0 < a < b$ cannot be differentiable
- $0$
- $1$
- $2$
- $3$
The Correct Option is C
Solution and Explanation
Top Questions on Continuity and differentiability
Let $ \mathbb{R} $ denote the set of all real numbers. Define the function $ f: \mathbb{R} \to \mathbb{R} $ by $$ f(x) = \begin{cases} 2 - 2x^2 - x^2 \sin\left(\frac{1}{x}\right), & \text{if } x \ne 0, \\ 2, & \text{if } x = 0. \end{cases} $$ Then which one of the following statements is TRUE?
- JEE Advanced - 2025
- Mathematics
- Continuity and differentiability
- Evaluate the following statement: \[ f(x) = \sin(|x|) - |x| \text{ is not differentiable at } x = \underline{\hspace{2cm}} \]
- KEAM - 2025
- Mathematics
- Continuity and differentiability
- Evaluate the derivative of the function: \[ f(x) = x |x|, \quad \text{find} \quad f'(-10) \]
- KEAM - 2025
- Mathematics
- Continuity and differentiability
- A function \( f \) is defined by \( f(x) = 2 + (x - 1)^{2/3} \) on \( [0, 2] \). Which of the following statements is incorrect?
- WBJEE - 2025
- Mathematics
- Continuity and differentiability
- Let \( f(x) = |1 - 2x| \), then:
- WBJEE - 2025
- Mathematics
- Continuity and differentiability
Questions Asked in WBJEE exam
- Which logic gate is represented by the following combination of logic gates?
- WBJEE - 2025
- Logic gates
- If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:
- WBJEE - 2025
- permutations and combinations
- If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:
- WBJEE - 2025
- Trigonometric Equations
- Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
- If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then
- WBJEE - 2025
- Quadratic Equations
WBJEE Notification
Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.