Calculus I: The Quotient Rule (Level 3 of 3)

The video tutorial covers finding derivatives using both sets of values and graphs. It begins with an introduction to the concept of derivatives and the use of the quotient rule. The tutorial provides examples of finding derivatives using given values and applying the quotient rule. It also demonstrates how to find derivatives using graphs, emphasizing the geometric interpretation of derivatives as slopes of tangent lines. The video concludes with a reminder to use the quotient rule for functions formed by quotients.

What rule is applied to find the derivative of a function formed by the quotient of two functions?

• Quotient Rule

• Chain Rule

• Product Rule

• Reciprocal Rule

In the example where f(x) = h(x)/x, what is the value of f'(2) given h(2) = 4 and h'(2) = -3?

• -5

• 5

• 3

• -3

When finding the derivative of x = 1/g(x), which rule could also be used besides the quotient rule?

• Product Rule

• Power Rule

• Reciprocal Rule

• Chain Rule

What is the final value of f'(0) when g(0) = 2 and g'(0) = 1 for the function x = 1/g(x)?

• 14

• -7

• -14

• 7

How is the derivative of a function represented geometrically on a graph?

• As the y-coordinate of the function

• As the x-coordinate of the function

• As the area under the curve

• As the slope of the tangent line

In the example using graphs, what is the value of q'(4) when f(4) = 7, g(4) = 3, f'(4) = -1, and g'(4) = 0?

• -1/3

• 1/3

• -3

• 3

For the final example, what is the value of q'(7) when f(7) = 4, g(7) = 4, f'(7) = 2, and g'(7) = -1?

• 1/2

• 3/4

• 1/4

• 2/3