# Worksheet: Graphing Using Derivative

Q1:

The graph of a function is shown. At which point is negative but positive?

• Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint

Q2:

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

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

Q3:

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

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

Q4:

The graph of the first derivative of a function is shown. On what intervals is concave upward or concave downward?

• A is concave upward on and and concave downward on and .
• B is concave upward on , , and and concave downward on , , and .
• C is concave upward on and and concave downward on and .
• D is concave upward on , , and and concave downward on , , and .
• E is concave upward on and and concave downward on and .

Q5:

Determine the local maximum and minimum values of the function .

• Alocal minimum , local maximum
• Blocal maximum , local minimum
• Clocal maximum , local minimum
• Dlocal minimum , local maximum

Q6:

Determine the local maximum and minimum values of the function .

• Alocal minimum , local maximum
• Blocal maximum , local minimum
• Clocal maximum , local minimum
• Dlocal minimum , local maximum

Q7:

Determine where is concave up and/or where it is concave down.

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

Q8:

Determine where is concave up and/or where it is concave down.

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

Q9:

Find, if they exist, the local maximum and/or minimum values of the function . Also specify what type of value they are.

• Ahas no local maximum or minimum points
• B , local maximum value
• C , local maximum value
• D , local minimum value
• E , local minimum value

Q10:

Find, if they exist, the local maximum and/or minimum values of the function . Also specify what type of value they are.

• Ahas no local maximum or minimum points
• B , local maximum value
• C , local maximum value
• D , local minimum value
• E , local minimum value

Q11:

Determine where the curve defined by and , , is concave upward and where it is concave downward.

• A The curve is concave upward on the interval .
• B The curve is concave downward on the interval and upward on the interval .
• C The curve is concave downward on the interval .
• D The curve is concave downward on the interval and upward on the interval .
• E The curve is concave downward on the interval and upward on the interval .

Q12:

Let Find the intervals on which the graph is convex downwards and on which it is convex upwards.

• A convex downwards on, convex upwards on
• B convex upwards on, convex downwards on
• C convex downwards on and , convex upwards on
• Dconvex upwards on and , convex downwards on

Q13:

Let Find the intervals on which the graph is convex downwards and on which it is convex upwards.

• A convex downwards on, convex upwards on
• B convex upwards on, convex downwards on
• C convex downwards on and , convex upwards on
• Dconvex upwards on and , convex downwards on

Q14:

Find where (if at all) the function has its local maxima and minima.

• Alocal minimum at , no local maximum
• Blocal minimum at , local maximum at
• Clocal maximum at , no local minimum
• Dlocal maximum at , local minimum

Q15:

Find where (if at all) the function has its local maxima and minima.

• Alocal minimum at , no local maximum
• Blocal minimum at , local maximum at
• Clocal maximum at , no local minimum
• Dlocal maximum at , local minimum

Q16:

For find the intervals on which is increasing or decreasing.

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

Q17:

For find the intervals on which is increasing or decreasing.

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