Lindsey's Reflection

This week we learned about optimization.

here are the steps in solving an optimization
problem:

1. identify all given quanities and what
you are to find.

2. find a primary equation:
**hint-it is the one that is closest
to the word maximize or minimize.

3. find a secondary equation if necessary
(only if there are two variables in the
equation in step two)

4. find a max or min by plugging into
the primary equation and do the first
derivative test. instead of intervals
plug back into primary equation to
find the highest and lowest value.

here is an example applying these steps:

Find two non-negative numbers whose
sum is 9 and so the product of one number
and the square of the other number is
a maximum.

1. a + b=9 P=a x b^2

2. p= a x b^2--primary equation

3. a + b=9 b=9-a

4. p= a(9-a)^2

p= a (81-18a+a^2)
=81a-18a^2+a^3

81+36a+3a^2=0
3(a^2-12a+27)=0
(a-3) (a-9)

a=3,9

3=108--max
9=0

108=3 x b^2

a=3
b=6

not too hard. goodnight.