 ##### Asked by: Sohayb Hugas
asked in category: General Last Updated: 29th April, 2020

# What does the slope of a tangent line represent?

A 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 x2 2x

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