Understanding Tangent Lines and Slopes

The video tutorial explains how to determine the points on the graph of the function f(x) = -1/x where the tangent lines are parallel to the line y = 2x + 4. It begins by identifying the slope of the given line and then calculates the derivative of the function to find the slopes of the tangent lines. The tutorial proceeds to solve for the X values where the slope of the tangent lines equals 2, and then finds the corresponding Y coordinates. Finally, it verifies the points on the coordinate plane and concludes by confirming that the tangent lines at these points are parallel to the given line.

What is the slope of the line y = 2x + 4?

• 1

• 2

• 3

• 4

Why do parallel lines have the same slope?

• Because they never intersect

• Because they are perpendicular

• Because they intersect at one point

• Because they have different slopes

What is the derivative of f(x) = -1/x using the power rule?

• -x^2

• x^2

• -1/x^2

• 1/x^2

What is the purpose of finding the derivative of a function?

• To find the area under the curve

• To determine the slope of tangent lines

• To calculate the volume of a solid

• To find the maximum value of a function

What equation do we solve to find the x-values where the slope of the tangent lines is 2?

• 1/x^2 = 2

• x = 2

• 1/x = 2

• x^2 = 2

What are the solutions for x when solving 1/x^2 = 2?

• x = ±1/√2

• x = ±1

• x = ±2

• x = ±√2

How do you find the y-coordinates for the x-values obtained?

• By solving a new equation

• By differentiating the function again

• By integrating the function

• By substituting x-values into the original function

What is the approximate decimal value of -1/√2?

• -1.414

• -0.5

• -0.707

• -2

Why is it important to convert coordinates to decimals for plotting?

• To change the slope of the line

• To simplify the function

• To accurately locate points on the coordinate plane

• To make calculations easier

What should be the relationship between the tangent lines and the line y = 2x + 4 at the points found?

• They should overlap

• They should intersect

• They should be parallel

• They should be perpendicular