Understanding Secant and Tangent Lines

Professor Dave introduces differentiation, a key concept in calculus, by exploring how to find the equation of a tangent line to a curve. He uses the example of the parabola y = x^2 and the point (1, 1) to demonstrate the process. By calculating the slope of secant lines and refining it, he shows how to approach the slope of the tangent line, ultimately finding it to be 2. This process illustrates differentiation and the rate of change at a point.

What is the main concept introduced in the video?

• Integration

• Geometry

• Differentiation

• Algebra

What does the term 'tangent' mean in the context of a curve?

• A line that intersects the curve at two points

• A line that intersects the curve at one point

• A line that is parallel to the curve

• A line that does not touch the curve

Which curve is used as an example in the video?

• y = 1/x

• y = x

• y = x^2

• y = x^3

What are the coordinates of the point chosen on the curve y = x^2?

• (0, 0)

• (3, 9)

• (2, 4)

• (1, 1)

What is the formula for the slope of a line between two points?

• y1 - y2 over x1 - x2

• x1 - x2 over y1 - y2

• y2 - y1 over x2 - x1

• x2 - x1 over y2 - y1

What is the slope of the secant line when x = 2?

• 2

• 3

• 4

• 1

What happens to the slope of the secant line as the second point gets closer to (1, 1)?

• It gets closer to 1

• It gets closer to 0

• It gets closer to 2

• It gets closer to 3

What is the slope of the tangent line at the point (1, 1) on the curve y = x^2?

• 2

• 4

• 1

• 3

What is the y-intercept of the tangent line at the point (1, 1) on the curve y = x^2?

• 2

• -1

• 0

• 1

What is the equation of the tangent line at the point (1, 1) on the curve y = x^2?

• y = 2x + 1

• y = x - 1

• y = 2x - 1

• y = x + 1