# Worksheet: Applications to Sketching Graphs

Q1:

Determine the critical points of the function in the interval rounded to one decimal place.

• A, .
• B, .
• C, .
• D, .
• E, .

Q2:

Determine the local maximum and minimum values of the function .

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

Q3:

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

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

Q4:

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

• A, local minimum value
• B, local maximum value
• C, local minimum value
• Dhas no local maximum or minimum points
• E, local maximum value

Q5:

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

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

Q6:

For find the intervals on which is increasing or decreasing.

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

Q7:

Find the exact value of at which increases most rapidly if .

• A
• B
• C
• D
• E

Q8:

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 .

Q9:

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

• AThe function is concave up on the interval and concave down on the interval .
• BThe function is concave up on the interval and concave down on the interval .
• CThe function is concave up on the interval and concave down on the interval .
• DThe function is concave up on the interval and concave down on the interval .
• EThe function is concave up on the interval and concave down on the interval .

Q10:

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

• AThe function is concave down on the interval .
• BThe function is concave up on the interval .
• CThe function is concave down on the interval .
• DThe function is concave down on the interval .
• EThe function is concave up on the interval .

Q11:

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

• AThe function is concave up on and concave down on .
• BThe function is concave up on and concave down on .
• CThe function is concave up on and concave down on .
• DThe function is concave up on and concave down on .
• EThe function is concave up on and concave down on .

Q12:

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

• Aconvex downwards on and , convex upwards on
• Bconvex upwards on and , convex downwards on
• Cconvex downwards on, convex upwards on
• Dconvex upwards on, convex downwards on

Q13:

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

• AThe curve is concave downward on the interval and upward on the interval .
• BThe curve is concave downward on the interval .
• CThe curve is concave downward on the interval and upward on the interval .
• DThe curve is concave upward on the interval .
• EThe curve is concave downward on the interval and upward on the interval .

Q14:

Find the vertical and horizontal asymptotes of the function .

• AThe function has no vertical asymptote and a horizontal asymptote at .
• BThe function has a vertical asymptote at and no horizontal asymptote.
• CThe function has no vertical asymptote and a horizontal asymptote at .
• DThe function has no vertical asymptote and a horizontal asymptote at .
• EThe function has a vertical asymptote at and no horizontal asymptote.

Q15:

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

• Apoint
• Bpoint
• Cpoint
• Dpoint
• Epoint