Finding a symmetric interval The function f in the figure satisfies lim xS4 f 1x2 = 5. For each value of e, find all values of d 7 0 such that _ f 1x2 - 5 _ 6 e whenever 0 6 _ x - 4 _ 6 d. (3) a. e = 2 b. e = 1 c. For any e 7 0, make a conjecture about the corresponding value of d satisfying (3).

Calculus notes for week of 9/19/16 3.6 Derivatives as Rates of Change Velocity is measured as: V ave(t+∆t) or s(b) – s(a) ∆t b – a (Change in position over change in time.) S’’(t) = V’(t) = A(t) (From left to right: S=Position, V= Velocity, and A=Acceleration) Average and Marginal Cost Suppose C(x) gives the total cost to produce x units of a good cost. Sometimes, C(x) = FC + VC * x FC = Fixed cost which does not change with units produced. VC = Variable cost which is the cost to produce each unit. C(x) = Average cost. C’(x) = Marginal cost, which is approximately the extra cost to produce one more unit beyond x units. C’(x) = lim C(x+∆x) – C(x) ∆x>0 ∆x 3.7 Chain Rule How do we differentiate a composi