Question

7. (Lesson 3.5) Let S(x)=-8x+16, if x53 [ax+b, if x>3. Find a and b such that the function(x) is differentiable everywhere. (HINT: First use differentiability to find a. Then use continuity to find b.) M 8 . (Lesson 3.6) Memorize the following integration formulas, then practice using them. Power Rule: If n*-1, then ſx"dx = --***!+C Constant Multiple Rule: ſk. (x)=k[ /[x]cle Sum/Difference Rule: (x)£g(x)}!x = 5 /(x)det g(x) (b) f(6x–3Vx+dr = — (a) dr = — 9. (Lesson 3.6) Recall that (x]cle represents the infinite family of antiderivatives of S, each identified by its constant of integration, C. Given a point in the plane, we could find the constant C that identifies the unique member of the family passing through the given point. Consider the function f(x)= and suppose Fox) is the antiderivative of Ox) such that FD- - i.e., the graph passes through the point (1.-)). Then F(X) =

Answer 1

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