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MATH 1712: WEEK 7 PRACTICE PROBLEMS
1. Find
dy
dx
if y = (5x − 2)e1−2x .
2. Find two positive numbers, x and y, whose sum is 100 and whose product
is a large as possible.
3. A large soup can holds 16π in3 of soup. Find the dimensions of the
can that minimize the amount of metal used in its construction. NOTE:
The volume and surface area of a can are given by: V = πr2 h and SA =
2πr2 + 2πrh.
SOLUTIONS
1.
dy
dx
= 5e1−2x − (10x − 4)e1−2x
2. x = y = 50
3. r = 2 in, h = 4 in
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