Exploring Derivatives in AP Calculus AB

This video tutorial covers Unit 2 of Calculus AB, focusing on differentiation. It explains the concept of derivatives, including the rate of change, and introduces various forms and notations. The video discusses the relationship between continuity and differentiability, and presents key differentiation rules such as the power, product, and quotient rules. It also covers trigonometric differentiation and how to find equations for tangent and normal lines. The tutorial concludes with a summary and encourages viewers to practice the concepts.

What is the derivative of a function?

• The integral of a function

• The rate of change of a function

• The average value of a function

• The maximum value of a function

What does the secant line represent?

• The integral of the function

• The slope at one point of the function

• The slope between two points on the graph

• The maximum value of the function

Which of the following is a requirement for a function to be differentiable?

• The function must be increasing

• The function must be continuous

• The function must be decreasing

• The function must be bounded

What is the derivative of a constant?

• Zero

• The constant squared

• The constant itself

• One

How do you apply the power rule to find the derivative of x^5?

• Divide by 5 and subtract 1 from the exponent

• Multiply by 5 and add 1 to the exponent

• Divide by 5 and add 1 to the exponent

• Multiply by 5 and subtract 1 from the exponent

What is the derivative of e^x?

• 1/x

• x^e

• ln(x)

• e^x

Which rule is used to find the derivative of a product of two functions?

• Product rule

• Chain rule

• Quotient rule

• Power rule

What is the derivative of sin(x)?

• -cos(x)

• sin(x)

• -sin(x)

• cos(x)

How do you find the equation of a tangent line at a point?

• Use the integral of the function

• Use the slope-intercept formula with the derivative as the slope

• Use the point-slope formula with the derivative as the slope

• Use the quadratic formula

What is the normal line to a curve at a point?

• A line perpendicular to the tangent line

• A line that intersects the curve at two points

• A line parallel to the tangent line

• A line that is tangent to the curve at two points