Write the tangent line of an equation through a point

The video tutorial covers the product rule and its application in calculus. It begins with an introduction to the product rule and the importance of simplifying problems. The instructor demonstrates how to simplify a problem using the FOIL method and then applies the power rule to find the derivative. The tutorial explains how to find the equation of a tangent line at a specific point by calculating the slope using the derivative. The session concludes with finalizing and simplifying the tangent line equation, emphasizing the importance of accuracy in arithmetic calculations.

Why might the product rule not be the best approach for the given problem?

• It is too complex for this problem.

• The product rule is not applicable here.

• It requires additional steps.

• The problem can be simplified using FOIL.

What is the purpose of simplifying the equation before taking the derivative?

• To make the equation longer.

• To make it easier to apply the power rule.

• To eliminate variables.

• To avoid using the product rule.

What is the derivative of the simplified equation?

• 3X^2 + 6X + 2

• X^3 + 3X^2 + 2X

• 2X^2 + 4X + 1

• X^2 + 2X + 3

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

• By simplifying the equation.

• By guessing the slope.

• By calculating the derivative at that point.

• By using the product rule.

What is the equation of the tangent line at the point (1, 6)?

• y - 6 = 11(x - 1)

• y = 11x + 6

• y = 6x + 11

• y - 1 = 6(x - 11)