##### Asked by: Sohayb Hugas

asked in category: General Last Updated: 29th April, 2020# What does the slope of a tangent line represent?

**tangent line**is a straight

**line**that touches a function at only one point. The

**tangent line represents**the instantaneous rate of change of the function at that one point. The

**slope**of the

**tangent line**at a point on the function is equal to the derivative of the function at the same point (See below.)

Similarly, you may ask, why does the derivative represent the slope of a tangent line?

The **Derivative** Measures **Slope** By plugging in different input values, x = a, the output values of f '(x) give you the **slopes** of the **tangent lines** at each point x = a. This is what we mean when we say that “the **derivative** measures the **slope** of the **tangent lines**.”

Likewise, is the derivative the slope of a tangent line? Thus, the **derivative** is a **slope**. This is the same as saying that the **derivative** is the **slope** of the **tangent line** to the graph of the function at the given point. The **slope** of a secant **line** (**line** connecting two points on a graph) approaches the **derivative** when the interval between the points shrinks down to zero.

Additionally, what does the slope of a tangent line on a position time graph represent?

The **slope** at any point on a **position**-versus-**time graph** is the instantaneous **velocity** at that point. It is found by drawing a straight **line tangent** to the **curve** at the point of interest and taking the **slope** of this straight **line**. **Tangent lines** are shown for two points in Figure.

What is the derivative of 1?

The **Derivative** tells us the slope of a function at any point. There are rules we can follow to find many **derivatives**. For example: The slope of a constant value (like 3) is always 0.

**Derivative** Rules.

Common Functions | Function | Derivative |
---|---|---|

Constant | c | 0 |

Line | x | 1 |

ax | a | |

Square | x^{2} | 2x |