Applications of Derivatives Review

Which of the following best describes the continuity at x = 5?

• Continuous
• Removable Point Discontinuity
• Non-removable Infinite Discontinuity
• Non-removable Jump Discontinuity

Which of the following best describes the continuity at x = 1?

• Continuous
• Removable Point Discontinuity
• Non-removable Infinite Discontinuity
• Non-removable Jump Discontinuity

Tags

CCSS.HSF-IF.C.7B

Which of the following must be true for a function to be continuous at a point, a? (select all that apply)

• f(a) must exist

• the limit as x approaches a must exist

• the function has to go to infinity

• f(a) and the limit as x approaches a must be equal

• you won't need to do any factoring/simplifying when finding the limit

Tags

CCSS.HSF-IF.C.7D

For what value(s) of x is the function continuous but not differentiable?

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

Is the function continuous, differentiable, both, or neither?

• continuous

• differentiable

• both

• neither

Is the function continuous, differentiable, both, or neither?

• continuous

• differentiable

• both

• neither

Tags

CCSS.HSF-IF.C.7B

Find the values of a and b that make the function f differentiable.

(a)  

Find the values of a and b that make the function f differentiable.

(a)  

The function g is continuous on the interval [0, 5] and has select values in the table. The equation g(x) = 1 must have at least 2 solutions in the interval [0, 5] if k = ?



• 6

• 0

• 2

• 1

Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that

• f(c)=2 for at least one c between -3 and 1

• f(c)=0 for at least one c between -2 and 5

• f(c)=0 for at least one c between -3 and 1

• f(c)=2 for at least one c between -2 and 5