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

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) (Show Source): You can put this solution on YOUR website!
Just minimize the function. Calculating f'(x), we get

since

Setting it to 0, we get

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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