# mid2e - Applied Calculus(Math 215 Midterm 2 Problem 1[5...

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Applied Calculus (Math 215) – Midterm 2 Problem 1. [5 Points] State the Second Derivative Test for ﬁnding local extrema of a function f ( x ). Problem 2. [5 Points] State what it means that a function f ( x )isconcave up on an interval I . Illustrate your deﬁnition with the picture of an example. Problem 3. [10 Points] Solve the initial value problems: (a) f 0 ( x )=2 x +sec 2 x and f ( π/ 4) = 1. (b) g 0 ( x )=3 g ( x )and g (5)=1. Problem 4. [20 Points] Cut a string of length 1 meter into two pieces. Use one piece to form a circle (the perimeter of a disk) and one as the perimeter of a square. How should the string be cut so that the combined area of the square and disk is maximal? What is the largest possible combined area? How should the string be cut, so that the combined area of the square and the disk is minimal? What is the smallest possible combined area? Problem 5. [35 Points] Consider the function f ( x )= x 3 - 4 x +3.

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## This note was uploaded on 07/26/2009 for the course MATH 215 taught by Professor Heiner during the Spring '09 term at Hawaii.

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mid2e - Applied Calculus(Math 215 Midterm 2 Problem 1[5...

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