1. Review for Test 3 Glendale Community College Phong Chau

2. Graphs of Functions Find the interval of increase/decrease.  f ’(x) > 0, f(x) is increasing  f ’(x) < 0, f(x) is decreasing Find the relative extrema.  Use test values

3. Graphs of Functions Find the interval of concavity.  f ’’(x) > 0, f(x) is concave up. + +  f ’’(x) < 0, f(x) is concave down. – – Find the inflection points.  Inflection point occurs at the point where the second derivative changes sign. Sketch the graph showing all important features of the curve.

4. Absolute Extrema Find absolute maximum/minimum of f(x) on a closed interval [a, b] 1. Find the critical numbers of f(x) 2. Evaluating the functions at critical numbers and at the end points a and b. 3. The largest values in step 2 is the absolute maximum, and the smallest value is the absolute minimum

5. Implicit Differentiation 1. Differentiate both sides of an equation 2. Find an equation of a tangent line

6. Application Problems 1. Optimization Problem (14.2) 2. Related Rates Problem (14.5) 3. Elasticity of Demand (14.3)

7. Examples Find the interval of increase/decrease. relative extrema, intervals of concavity, and inflection points

8. Examples Find the absolute extrema for The cost (in thousands) function of an auto parts is given by Find the minimum value of the average cost.

9. Examples The demand for beer is given by the demand function Find the elasticity of demand function Find and interpret the elasticity of demand at p = $6.

10. Examples A fence must be build to enclose a rectangular area of 20,000 sq. ft. Fencing material costs $2.50 per foot for the two sides facing north and south, and $3.20 per foot for the other two sides. Find the cost of the least expensive fence.