Week 11 Calculus I Outline of Notes

by S. Gramlich

(updated 12/11/06)

 

I)          4.7 Optimization

            1) Reread

            2) Diagram

            3) Write Given & define variable

            4) Write Formulas (use inner flap of text)

            5) Substitute 1 eqn into other to get eqn in terms of 1 varb & find Domain (endpoints)

            6) Find critical #s (set derivative = 0 & solve)

            7) Use Closed Interval Method (4.1, p. 283)

            OR 1st Derivative Test (4.3, p. 297 or 4.4, p. 334) to find Absolute Extrema

                        *Note:  Abs Max/Min is dv value

            4.7, Example 1, p. 332

            4.7, Example 2, p. 333

 

II)        4.10 Antiderivatives= reverse differentiation;

            start with nth derivative fn(x) then find original function F(x)+C,

where C allows for a family of functions

see Table of Antidifferentiation Formulas, p. 354

especially f’(x)=xn => F(x)= x(n+1)/(n+1)

4.10, p. 358, #22, 62