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

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