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

Q3:

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

Q4:

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

Q5:

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 .

Q6:

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 .

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.

  • 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 .

Q10:

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 .

Q11:

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 .

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:

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 .

Q14:

Find the vertical and horizontal asymptotes of the function .

  • A The function has no vertical asymptote and a horizontal asymptote at .
  • B The function has a vertical asymptote at and no horizontal asymptote.
  • C The function has a vertical asymptote at and no horizontal asymptote.
  • D The function has no vertical asymptote and a horizontal asymptote at .
  • E The function has no vertical asymptote and a horizontal asymptote at .

Q15:

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

  • Apoint
  • Bpoint
  • Cpoint
  • Dpoint
  • Epoint