B determine on which intervals the graph of f is

This preview shows page 3 - 7 out of 9 pages.

(b) Determine on which intervals the graph offis increasing, and on which intervals it is decreasing.You may use the fact thatf0(x) =10 (1°2 lnx)x3.(c) Determine on which intervals the graph offis concave up, and on which it is concave down.You may use the fact thatf00(x) =10 (6 lnx°5)x4.(d) Use the information found in parts (a) to (c) to sketch a graph ofy=f(x).Label any keyfeatures of the graph.-2-1123456-2-1123
6.[10marks]Use the Intermediate Value Theorem to show that the equationsin (x)°2x= 1°1p2has at least one solution in the open interval´°°4;0µ.Then use Rolle²s Theorem to prove that, infact, the equation has exactly one solution.4
7.[10marks]A rectangular box with an open top is to have a volume of 48 m3.The length of the baseis to be twice the width.The material for the base costs $8 per square metre.Material for the sideswill cost $6 per square metre.Find the cost of producing the cheapest such box.5
8.[8marks]Use a Riemann sum with a regular partition to determine(x+ 3)2dx.6R

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture