Tangent Line and Derivative Concepts

The video tutorial explains how to find the equation of a tangent line to a function at a given point. It covers rewriting the function using rational exponents, finding the derivative, evaluating the slope at a specific point, and deriving the equation of the tangent line using point-slope and slope-intercept forms. The tutorial concludes with a graphical verification of the results.

What is the first step in finding the equation of a tangent line to a function?

• Determine the y-intercept of the function

• Find the derivative of the function

• Calculate the area under the curve

• Identify the x-intercept of the function

How can the square root of x be expressed using exponents?

• x to the power of 2

• x to the power of -1/2

• x to the power of 1/2

• x to the power of 3/2

What is the derivative of 4x?

• 2x

• x

• 0

• 4

What is the simplified form of the derivative of 7x^(1/2)?

• 7/2 * x^(1/2)

• 7x^(-1/2)

• 7x^(1/2)

• 7/2 * x^(-1/2)

What is the slope of the tangent line at the point (4, 2)?

• 9/4

• 7/4

• 4/9

• 2

Which form of the equation is used first to find the tangent line?

• Slope-intercept form

• Standard form

• Quadratic form

• Point-slope form

What is the y-intercept of the tangent line in slope-intercept form?

• 0

• 2

• 9/4

• -7

How is the slope of the tangent line verified graphically?

• By comparing with another line

• By checking the x-intercept

• By observing the vertical intercept

• By moving up 9 units and right 4 units

What is the significance of the point (4, 2) in the context of the tangent line?

• It is the point of tangency

• It is the x-intercept of the tangent line

• It is the midpoint of the tangent line

• It is the y-intercept of the tangent line

What does the red line represent in the graphical verification?

• The original function

• The tangent line

• The y-axis

• The x-axis