# Worksheet: Consequences of Differentiability

Q1:

The graph of the first derivative of a continuous function is shown. On what intervals is increasing or decreasing?

• A is increasing on the intervals and and decreasing on the interval .
• B is increasing on the intervals and and decreasing on the intervals , , and .
• C is increasing on the interval and decreasing on the intervals and .
• D is increasing on the intervals , , and and decreasing on the intervals and .
• E is increasing on the intervals and and decreasing on the intervals and .

Q2:

Determine the intervals on which the function is increasing and where it is decreasing.

• A increasing over
• Bdecreasing over , increasing over
• C decreasing over
• Dincreasing over , decreasing over

Q3:

Which of the following statements is true for the function ?

• A is increasing on and decreasing on .
• B is increasing on and decreasing on .
• C is increasing on and decreasing on .
• D is increasing on and decreasing on .
• E is increasing on and decreasing on .

Q4:

Which of the following statements is true for the function ?

• A is increasing on and decreasing on .
• B is increasing on and decreasing on .
• C is increasing on and decreasing on .
• D is increasing on and decreasing on .
• E is increasing on and decreasing on .

Q5:

Determine the intervals on which the function is concave up and down.

• A The function is concave down on and concave up on .
• B The function is concave down on and concave up on .
• C The function is concave down on and and concave up on .
• D The function is concave down on and concave up on .
• E The function is concave down on and concave up on .

Q6:

The graph of a function is shown. At which point are and both positive?

• Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q7:

The graph of a function is shown. At which point are and both negative?

• Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q8:

Determine the intervals on which is concave up and concave down.

• A The function is concave up on the interval and concave down on the interval .
• B The function is concave up on the interval and concave down on the interval .
• C The function is concave up on the interval and concave down on the interval .
• D The function is concave up on the interval and concave down on the interval .
• E The function is concave up on the interval and concave down on the interval .

Q9:

Let . Determine the intervals where this function is increasing and where it is decreasing.

• A The function is decreasing on and and increasing on .
• B The function is decreasing on and increasing on and .
• C The function is decreasing on and and increasing on .
• D The function is decreasing on and and increasing on .
• E The function is decreasing on and increasing on and .

Q10:

Let . Determine the intervals where this function is increasing and where it is decreasing.

• A The function is decreasing on and and increasing on .
• B The function is decreasing on and increasing on and .
• C The function is decreasing on and and increasing on .
• D The function is decreasing on and and increasing on .
• E The function is decreasing on and increasing on and .

Q11:

The graph of the first derivative of a continuous function is shown. On what intervals is increasing or decreasing?

• A is increasing on the intervals , , and and decreasing on the intervals and .
• B is increasing on the intervals and and decreasing on the intervals and .
• C is increasing on the intervals and and decreasing on the intervals , , and .
• D is increasing on the intervals and and decreasing on the intervals and .
• E is increasing on the intervals and and decreasing on the intervals and .

Q12:

Which of the following statements is true for the function ?

• AThe function is decreasing on.
• BThe function is decreasing on and increasing on.
• CThe function is increasing on.
• DThe function is increasing on and decreasing on.