Tangent Lines and Derivatives

The video tutorial explains how to find the equation of a tangent line to a curve at a specific point. It covers identifying the x and y coordinates, calculating the slope using the derivative, and applying the quotient rule. The process includes simplifying the derivative expression and evaluating it at a given point. Finally, the tutorial demonstrates how to write the equation of the tangent line using the point-slope form.

What is the first step in writing the equation of a tangent line?

• Finding the x-coordinate

• Finding the midpoint

• Finding the slope

• Finding the y-intercept

How do you find the y-coordinate when x = 1?

• By using the formula y = mx + b

• By using the midpoint formula

• By substituting x = 1 into the function

• By finding the derivative

What is the coordinate point found when x = 1?

• (1, 3/2)

• (1, 2/3)

• (1, 1/3)

• (1, 1/2)

What is the purpose of finding f'(x) in this context?

• To find the slope of the tangent line

• To find the x-intercept

• To find the midpoint

• To find the y-intercept

What is the derivative of a constant?

• One

• Zero

• The constant itself

• Undefined

What is the derivative of x to the negative first power?

• 1/x^2

• -x^2

• 1/x

• -1/x^2

What is the value of f'(1) in this problem?

• -1/3

• 1/3

• -1/9

• 1/9

What is the equation of the tangent line derived in this lesson?

• y - 1/3 = 1/9(x - 1)

• y - 1/3 = 1/3(x - 1)

• y - 1/3 = -1/9(x - 1)

• y - 1/3 = -1/3(x - 1)