Plotting functions and tangents

This example demonstrates how to plot a function and draw a tangent line at a point. We'll work with the function y = x · sin(x) and explore how to visualize both the function and its tangent at any point.

Define the function

First, let's define our function y = x · sin(x). We'll use the variable x as our input:

• Define x value: x = \scalar 4

Now calculate y using the sine function:

• Calculate sin(x): sin-x = \sin x
• Calculate y = x · sin(x): y = \mul x sin-x

Other minor setup

Define colors:

• red
• Gray

Hide the origin point p0:

• Hide origin point

Set animation speed:

• Animation speed = 0.001

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Plot the entire function

To see the full function curve, we can use the plot command directly with our x and y variables:

• Plot the function: \plot x y
• Change its color

You could give a name to the plot (eg my-plot = \plot x y). However a name is auto-assigned when not provided. To know the auto-assigned name, just hover the mouse anywhere over the plot. In this case, the auto-assigned name must be plot0.

Create points and draw the function line

Let's create a point at (x, 0) on the x-axis and a point at (x, y) on the function:

• Point on x-axis
• Point on function
• Join the two points: \line p-x-axis p-func

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Draw the tangent line

The tangent command automatically calculates the derivative and draws the tangent line at the given x coordinate on the plot:

• Draw tangent:
• Hide points on the tangent line
• Set the color of the tangent line to white

Animate the point

Let's animate x from -4 to 4 to see how the tangent line changes as we move along the function:

• Animate x to 4

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Calculating gradients with broadcasting

One can also use an array of points as input to tangent function.

• Hide line joining input and output point
• Define xs
• Draw tangents
• Set their colors