Understanding Tangent Lines and Derivatives

The video tutorial explains how to find the equation of a tangent line to the function y = x * cube root of x that is parallel to the line y = 4x - 3. It involves rewriting the function to a suitable form, finding its derivative using the power rule, and solving for the point of tangency where the derivative equals the slope of the given line. The tutorial then demonstrates how to use point-slope form to derive the tangent line equation and verifies the solution graphically.

What is the slope of the line that the tangent line must be parallel to?

• 5

• 4

• 3

• 2

How is the function y = x * cube root of x rewritten for differentiation?

• y = x^3

• y = x^(1/3)

• y = x^(4/3)

• y = x^2

What rule is applied to find the derivative of the function?

• Chain Rule

• Power Rule

• Quotient Rule

• Product Rule

What is the x-coordinate of the point where the tangent line is parallel to the given line?

• 9

• 27

• 36

• 18

What operation is performed to solve for x from x^(1/3) = 3?

• Take the square root

• Cube both sides

• Take the cube root

• Square both sides

What is the y-coordinate of the point of tangency?

• 54

• 72

• 81

• 90

What is the slope of the tangent line at the point of tangency?

• 2

• 3

• 5

• 4

What is the point-slope form of the tangent line equation?

• y - 27 = 3(x - 81)

• y - 81 = 3(x - 27)

• y - 27 = 4(x - 81)

• y - 81 = 4(x - 27)

What is the slope-intercept form of the tangent line equation?

• y = 4x + 27

• y = 4x - 27

• y = 3x - 27

• y = 3x + 27

How is the solution verified graphically?

• By checking the collinearity of points

• By checking the perpendicularity of lines

• By checking the parallelism of lines

• By checking the intersection of lines