SOLUTION: Find two numbers whose difference is 60 and whose product is as small as possible. [hint: let x and x-60 be the two numbers. their product can be described by the function f(x)=x(x

Algebra ->  Expressions -> SOLUTION: Find two numbers whose difference is 60 and whose product is as small as possible. [hint: let x and x-60 be the two numbers. their product can be described by the function f(x)=x(x      Log On


   

Question 962755: Find two numbers whose difference is 60 and whose product is as small as possible. [hint: let x and x-60 be the two numbers. their product can be described by the function f(x)=x(x-60).]
Answer by hkwu(60) About Me  (Show Source):
You can put this solution on YOUR website!
Just minimize the function. Calculating f'(x), we get
d%2F%28dx%29%2Af%28x%29=2x-60
since
f%28x%29=x%5E2-60x
Setting it to 0, we get
2x-60=0
2x=60
x=30
You can do the first derivative test to make sure it is actually a minimum point. If x = 30, then
x - 60 = -30
and thus the two numbers are 30, -30.
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