Calculus Theorems

• TRUE

• FALSE

• CANNOT BE DETERMINED

• TRUE because there is a sign change on the interval

• FALSE because there is no sign change on the interval

• TRUE because of the Intermediate Value Theorem

• FALSE because the function is discontinuous on the interval

Let f be a function that is continuous on the closed interval [2,4] with f(2) = 10 and f(4) = 20. Which of the following is guaranteed by the Intermediate Value Theorem?

• f(x) = 13 has at least one solution in the open interval (2,4)

• f(3) = 15

• f attains a maximum on the open interval (2,4)

• f(x) = 10 at some other value(s) of x other than x = 2

• Average Rate of Change
• Average Value of f
• Intermediate Value Theorem
• Rolle's Theorem

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• Mean value theorem
• Rolle's theorem
• Intermediate Value Theorem
• Fundamental Theorem of Calculus

The intermediate value theorem (IVT) is primarily concerned with which of the following?

• y-values

• first derivative values

• second derivative values

• x-values

Which of these sums up the Mean Value Theorem (MVT)?

Which of these is NOT a hypothesis of the Mean Value Theorem (MVT)?

• A closed interval

• A differentiable function

• A continuous function

• A twice-differentiable function

What does the Extreme Value Theorem remind us to do?

• Check the endpoints! They might be the max/min.

• Check the inflection points! They might be the max/min.

• Check the endpoints! They give the secant slope.

• Check the inflection points! They are when the derivative is 0.