Understanding Derivatives with a Graphing Calculator

This video tutorial demonstrates how to use a free online graphing calculator to graph a function and determine its derivative values at specific points. The tutorial covers entering the function, adjusting the graph view, calculating derivative values, and verifying the slopes of tangent lines at given x-values. The function used is f(x) = 1/3 x^3 - 4x + 2, and the derivative values are calculated at x = 0, x = 2, and x = -3.

What is the function given in the lesson that needs to be graphed?

• f(x) = 1/3 x^3 - 4x + 2

• f(x) = x^2 - 4x + 2

• f(x) = 1/2 x^3 - 4x + 1

• f(x) = 1/3 x^2 - 4x + 3

Which key is used for the exponent character in the graphing calculator?

• Shift 5

• Shift 6

• Alt 5

• Ctrl 6

What is the first step to calculate derivative values using the graphing calculator?

• Click the plot graphs button

• Adjust the window for better view

• Enter the function in the calculation window

• Click the calculation tab and select derivative

What is the derivative value f'(0) as calculated in the lesson?

• 5

• 3

• 0

• -4

What does f'(2) = 0 indicate about the slope of the tangent line?

• The slope is negative

• The slope is undefined

• The slope is positive

• The slope is zero

What is the derivative value f'(-3) as calculated in the lesson?

• 5

• 0

• -4

• 3

What does the slope of the tangent line at x = 0 represent?

• The slope of the tangent line

• A relative maximum

• A relative minimum

• A point of inflection

What is the significance of a horizontal tangent line at x = 2?

• It indicates a relative maximum

• It indicates a relative minimum

• It indicates a point of inflection

• It indicates a vertical tangent

What does a positive slope of the tangent line at x = -3 indicate?

• The function is constant

• The function is increasing

• The function is decreasing

• The function is undefined

What is the purpose of sketching the tangent line on the graph?

• To calculate the area under the curve

• To find the x-intercepts

• To determine the y-intercepts

• To verify the slope of the tangent line