1. C URVE S KETCHING section 3-A

2. Where the derivative is zero or the function does not exist. Critical Values

3. Use Extreme Value Theorem if on a closed interval [a,b] (f(x) has both a min and a max on the interval) Otherwise use the a)First derivative test b)Second derivative test Extrema: Maxima and Minima

4. 1) find all extrema on the interval [0,4] a) graphically

5. 1) cont find all extrema on the interval [0,4] b) algebraically

6. 2)Find the absolute extrema and the critical values for on [-1,2] a) graphically

7. 2)Cont. Find the absolute extrema and the x- values of the critical numbers for on [-1,2] b) algebraically

8. 3)Find the extrema for and determine the intervals where increasing and decreasing

9. Analyzing the graph of a function a)Domain and Range: All real numbers except ___ b)Extrema and the intervals where increasing and decreasing (first derivative test) c)Intercepts: where the graph crosses the x-axis and the y-axis d)Inflection points and the intervals where concave up and concave down (second derivative test) e)Symmetry 1.About the y-axis if even function 2.About the origin if odd function

10. Find all critical values f) Asymptotes- rational functions Vertical: set the denominator equal to zero and verify the limit tends to infinity Horizontal: Take the limit of the function as x approaches ±∞ Slant: occur when the degree of the numerator is one higher than the degree of the denominator. Use long division or synthetic division to find the line g) Graph- put it all together

11. H OME W ORK Page 169 # 11,13,14,17,20, 25, 33 and 41