B 5.5 - Differentiation of Logarithmic Functions 6. Differentiate the following functions: A. f(z)=In(8z+7) D. f(t) = 4t*In(9t) B. g(z) = 71n(z3)z E. g(t) = l(tt C. h(z)=In (eze) F. h(t) =2In (V22 4E +7) 7. Use logarithm laws to help differentiate the following functions: A f(@) = [z(z+5)(+7)] D. f(t) = In [V/3E+5(2t 5)!] B. g(z) =1n [(3z +2)"(4z ~ 9)'] E. g(t) = In (/7 +3) Vbz2 +7 g2 C. h(z) =In [Til] F. h(t)=In [m:l 8. Consider the function f(z) = zIn(z?). A. Find an equation of the tangent line to the graph of when z = 5. B. Discuss the behavior of f. (Find the intervals for which f is increasing, decreasing, and state the relative extrema) C. Discuss the concavity of f. (Find the intervals for which f is concave up, concave down, and state the inflection points) 9. Find the absolute extrema of g(z) = % on the interval [2,8]. Round to the nearest hundredth. n(z 10. The demand function for a certain model of yacht is p = 200 0.01z In(z) where = represents the number of yachts and p is the price per yacht in hundreds of dollars. A. Find the revenue function for this model of yacht. B. Find the marginal revenue function for this model of yacht. C. Evaluate your function from part B. when z = 500. Interpret your answer in a complete sentence with proper units