Derivability of a Function at a Point
When analyzing the derivability of a function at a specific point, it is important to consider both the left-hand and right-hand derivatives at that point. Let's explore the scenario where the right-hand derivative of a function at x = a does not exist, but the left-hand derivative exists.

Definition of Derivability
A function is said to be derivable at a point if both the left-hand and right-hand derivatives exist and are equal at that point. The derivative of a function at a point measures the rate at which the function changes at that point.

Right-Hand Derivative vs. Left-Hand Derivative
- The right-hand derivative at a point x = a measures the rate of change of the function as x approaches a from the right side.
- The left-hand derivative at a point x = a measures the rate of change of the function as x approaches a from the left side.

Scenario Analysis
- If the right-hand derivative at x = a does not exist, it indicates that the function has a sharp corner, vertical tangent, or some other discontinuity at that point from the right side.
- However, if the left-hand derivative exists at x = a, it implies that the function is well-behaved and smooth approaching a from the left side.

Conclusion
In this scenario, since the right-hand derivative does not exist at x = a but the left-hand derivative exists, we cannot conclude that the function is derivable at x = a. The existence of both left-hand and right-hand derivatives is crucial for a function to be considered derivable at a specific point.