Understanding Differentiation Part 1: The Slope of a Tangent Line

The video introduces differentiation, focusing on finding the equation of a tangent line to a curve. It explains the concept of a tangent line, which touches a curve at one point, and how to calculate its slope using secant lines. By moving a second point closer to the tangent point, the slope of the secant line approaches that of the tangent line. The video concludes by discussing the rate of change and its relation to differentiation.

What is the main goal when finding a tangent line to a curve?

• To find a line that is perpendicular to the curve

• To find a line that has exactly one point in common with the curve

• To find a line that is parallel to the curve

• To find a line that intersects the curve at two points

How do we initially calculate the slope of a line when only one point on the curve is known?

• By selecting another point on the curve to form a secant line

• By using the midpoint formula

• By assuming the slope is zero

• By using the formula for the area under the curve

What happens to the slope of the secant line as the second point approaches the initial point?

• The slope remains constant

• The slope decreases indefinitely

• The slope approaches a specific value

• The slope becomes undefined

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

• 1

• 2

• 3

• 4

What does finding the slope of the tangent line at a point tell us about the function?

• It tells us the average value of the function

• It tells us the minimum value of the function

• It tells us the rate of change of the function at that point

• It tells us the maximum value of the function