Understanding Derivatives and Graphing with Desmos

This lesson covers using Desmos to graph a function and determine derivative values. It begins with entering the function into Desmos, adjusting the graph view, and calculating derivatives at specific points. The lesson concludes with verifying these derivative values by examining the slopes of tangent lines at given x-values, using an animated Desmos graph.

What is the primary purpose of using Desmos in this lesson?

• To create statistical charts

• To graph functions and find derivative values

• To perform matrix operations

• To solve algebraic equations

Which function is entered into Desmos for graphing?

• f(x) = 1/3 x^3 - 4x + 2

• f(x) = 2x^2 - 3x + 5

• f(x) = x^3 - 2x^2 + x

• f(x) = x^2 + 2x + 1

What is the purpose of adjusting the graph window in Desmos?

• To add labels to the axes

• To save the graph as an image

• To change the color of the graph

• To get a better view of the function

How do you find the derivative value at x = 0 in Desmos?

• Enter f'(0) in cell four

• Enter f'(0) in cell two

• Enter f'(0) in the settings menu

• Enter f'(0) in cell one

What is the derivative value of f at x = 2?

• 2

• 0

• -4

• 5

What does a derivative value of zero indicate about the tangent line?

• The tangent line is curved

• The tangent line is diagonal

• The tangent line is horizontal

• The tangent line is vertical

How is the tangent line verified for x = -3?

• By checking if the slope is zero

• By observing the tangent line is vertical

• By ensuring the slope is positive five

• By confirming the slope is negative four

What tool is used to animate the tangent line in Desmos?

• The slider for variable 'a'

• The export function

• The graph settings menu

• The color palette

What is the significance of the blue line in the Desmos graph?

• It is a reference line for calculations

• It is the tangent line to the curve

• It shows the y-axis

• It represents the x-axis

What is the final step in verifying the derivative values?

• Re-entering the function

• Animating the tangent line

• Comparing with a calculator

• Checking the graph for errors