Write the equation of a line tangent to a polynomial through a point

The video tutorial explains how to write the equation of a tangent line using the point-slope form. It covers understanding and calculating the slope through limits, simplifying expressions using algebraic methods, and finding the slope at a specific point. The tutorial concludes with writing the final equation of the tangent line.

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

• Calculate the area under the curve

• Find the midpoint

• Determine the slope

• Identify the y-intercept

Which formula is used to define the slope of a function at a point?

• y = mx + b

• F = ma

• Limit as H approaches 0 of (F(X + H) - F(X)) / H

• Pythagorean theorem

What is the purpose of substituting X + H into the function?

• To find the y-intercept

• To calculate the derivative

• To determine the maximum value

• To simplify the equation

What mathematical concept is used to expand (X + H)^3?

• Binomial expansion

• Pythagorean theorem

• Quadratic formula

• Trigonometric identities

Why is it important to cancel out terms in the expanded expression?

• To find the y-intercept

• To calculate the area under the curve

• To simplify the expression for easier calculation

• To determine the maximum value

What is the slope of the tangent line at the point (2, 12)?

• 14

• 16

• 12

• 18

What is the final equation of the tangent line?

• y = 14x - 2

• y = 14x + 12

• y = 14x - 28

• y = 14x - 2 + 12