Exploring Free Response Strategies for AP Calculus

What is the interval on which function f is defined?

• [2, 8]

• [-1, 6]

• [-2, 8]

• [0, 10]

What is the value of F(2) as given in the problem?

• 1

• 2

• 3

• 0

At x=6, what is the nature of function f according to its first derivative?

• Absolute minimum

• Neither maximum nor minimum

• Relative minimum

• Relative maximum

Why does f have neither a maximum nor a minimum at x=6?

• F' is undefined at x=6

• F' is zero at x=6

• F' changes sign at x=6

• F' does not change sign at x=6

Which intervals indicate that the graph of f is concave down?

• (-2, 0) and (4, 6)

• (0, 2) and (6, 8)

• (2, 4) and (6, 8)

• (0, 4) and (4, 8)

What does a negative second derivative indicate about the concavity of function f?

• Linear behavior

• Concave up

• Concave down

• Inflection point

What rule is applied to solve the limit as x approaches 6 for the function f?

• Quotient rule

• Chain rule

• L'Hopital's rule

• Product rule

What is the derivative of the bottom expression in the limit calculation?

• x^2 + 5x - 6

• 2x + 5

• 2x - 5

• x^2 - 5x + 6

What is the absolute minimum value of f on the interval [-2, 8]?

• 0

• 1

• 2

• 3

Which method is used to determine the absolute minimum value of function f?

• Limit comparison

• Candidate's test

• Differentiation

• Integration