Chain Rule and Function Evaluation

The video tutorial explains how to use the chain rule to evaluate a function H(x) = F(G(x)) at a specific point and find its derivative. The instructor demonstrates how to read values from a table to calculate H(-2) and the derivative of H at -2. The process involves substituting values into the function and applying the chain rule to find the derivative. The video concludes with a summary of the results, showing that H(-2) equals 2 and the derivative at -2 is -4.

What is the main topic of the video?

• Graphing linear functions

• Solving quadratic equations

• Understanding integrals

• Finding the chain rule from a table

What is the function H(x) defined as?

• H(x) = F(x) + G(x)

• H(x) = F(G(x))

• H(x) = F(x) - G(x)

• H(x) = G(F(x))

How do you evaluate H(-2) using the table?

• By subtracting G from F

• By adding F and G values

• By finding G(-2) and then F(G(-2))

• By finding F(-2) directly

What is the value of G(-2) from the table?

• -2

• 2

• 1

• 0

What is the value of F(1) according to the table?

• 4

• 1

• 2

• 3

What is the value of H(-2)?

• 0

• 3

• 1

• 2

What rule is applied to find the derivative of H(x)?

• Power rule

• Chain rule

• Product rule

• Quotient rule

What is the derivative of the outside function in H(x)?

• F'(G(x))

• F(x)

• G'(x)

• G(x)

What is the value of G'(-2) from the table?

• 0

• 1

• 2

• -2

What is the value of F'(2) from the table?

• 0

• -1

• -2

• 2