The slope of tangent at any point (a,b) is also called as ........

Answer

To solve the question, we will identify the terminology used in calculus related to the slope of a tangent line at a point on a curve.

### Step-by-Step Solution:

1. **Understanding the Concept of Slope**:
- The slope of a line is a measure of its steepness. In the context of a curve, the slope of the tangent line at a given point gives us the rate of change of the function at that point.

**Hint**: Recall that the slope is often represented as "rise over run."

2. **Identifying the Function**:
- If we have a function represented as \( y = f(x) \), the slope of the tangent line at any point \( (a, b) \) on this curve can be determined using calculus.

**Hint**: Think about how we can find the slope of a function at a specific point using derivatives.

3. **Using Derivatives**:
- The derivative of the function \( f(x) \), denoted as \( \frac{dy}{dx} \) or \( f'(x) \), gives us the slope of the tangent line at any point \( x \). Therefore, at the point \( (a, b) \), the slope of the tangent line is \( f'(a) \).

**Hint**: Remember that the derivative represents the instantaneous rate of change of the function.

4. **Terminology**:
- The slope of the tangent line at any point on the curve is also referred to as the "gradient." This term is commonly used in mathematics to describe the steepness of a line.

**Hint**: Consider other contexts where the term "gradient" is used, such as in physics or geometry.

5. **Final Answer**:
- Therefore, we conclude that the slope of the tangent at any point \( (a, b) \) is also called the **gradient**.

### Final Answer:
The slope of the tangent at any point \( (a, b) \) is also called the **gradient**.