Name _____________________________

Period __________ Date _____________

Curve Sketching Review Worksheet

I. Sketch the following curves, indicating maximum and minimum points and points of inflection. Show all work and graph on a separate graph paper. Use graphing calculator only to check your work!

1.

2.

3.

For #3:

Derivative: _______________________________________

Increasing on ( _______, ________) , ( _______ , _______)

Decreasing on ( _______, ________)

Relative maximum at ( _______, ________)

Relative minimum at ( _______, ________)

Second derivative: ___________________________________

Concave Up on ( _______, ________)

Concave Down on ( _______, ________)

Point of Inflection at ( _______, ________)

II. Sketch a smooth curve illustrating the following characteristics or properties:

4. If y is a function of x such that y’ > 0 for all x and y” < 0 for all x, sketch the curve.

5. Sketch , given that

6. Sketch , given that

7. Sketch , given that

8. Sketch the function which is

Increasing on and

Decreasing on

Concave up on

Concave down on

Relative maximum at

Relative minimum at

Point of inflection at

9. Sketch the curve with

y-axis symmetry

horizontal asymptote: y = 0

vertical asymptotes: x = -2, x = 2

increasing on and

decreasing on and

concave up on

concave down on and

10. Sketch the curve which is

Increasing on and

Decreasing on

Tangent with undefined slope at the origin

Horizontal tangent at

Concave up for all x except x = 0

No concavity at (0,0)

Use the Graphing Calculator and substitute values for a, b, c, d, and e in the equation

to get each of the three types of curves illustrated.

11. 12. 13.

11. a = _________ b = _________ c = _________ d = _________ e = _________

12. a = _________ b = _________ c = _________ d = _________ e = _________

13. a = _________ b = _________ c = _________ d = _________ e = _________