# What is the derivative of a line?

## What is the derivative of a line?

The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line.

## What is the graph of a derivative?

Derivative Graph Rules The top graph is the original function, f(x), and the bottom graph is the derivative, f'(x). What do you notice about each pair? If the slope of f(x) is negative, then the graph of f'(x) will be below the x-axis. If the slope of f(x) is positive, then the graph of f'(x) will be above the x-axis.

**What is the derivative of a vertical line?**

A vertical line is not a function and it cannot have a derivative. If you describe the function of x with respect to y, then sure the derivative is dxdy=0.

### How do you look at a graph and find the derivative?

Choose a point on the graph to find the value of the derivative at. Draw a straight line tangent to the curve of the graph at this point. Take the slope of this line to find the value of the derivative at your chosen point on the graph.

### How do you find the tangent line?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

**Is the derivative a straight line?**

A straight line has a constant slope, so the derivative of a straight line is a constant function, thus if you plotted the derivative of a straight line youd get only a horizontal line.

#### Is the derivative of a straight line 0?

The derivative is the constant function y=0 because the straight line y=1 has slope 0.

#### What is the derivative of a horizontal line?

A horizontal tangent line is a mathematical feature on a graph, located where a function’s derivative is zero. This is because, by definition, the derivative gives the slope of the tangent line. Horizontal lines have a slope of zero.

**What is the derivative of a flat line?**

The graph of the constant function, f(x)=C, where C is a number, is a horizontal line. The slope of such a line is zero. So the derivative of any constant function, f(x)=C, is zero. Easy peasy.

## What does the graph of the first derivative tell us?

The first derivative of a function is an expression which tells us the slope of a tangent line to the curve at any instant. Because of this definition, the first derivative of a function tells us much about the function. If is positive, then must be increasing. If is negative, then must be decreasing.

## Is the tangent line the derivative?

The derivative is not the same thing as a tangent line. Instead, the derivative is a tool for measuring the slope of the tangent line at any particular point, just like a clock measures times throughout the day. With this in mind, you’ll have no trouble tackling tangent line problems on the AP Calculus exam!

**Is the derivative the slope?**

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.