SOLUTION: Find a positive number for which the sum of its reciprocal and four times its square is the smallest possible value. Show all work.

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Question 382139: Find a positive number for which the sum of its reciprocal and four times its square is the smallest possible value. Show all work.
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
Gives : 1/x+4x^2=f(x), f(x) has a minimum :

f'(x)=-1/x^2+8x=0 =>8x^3=1 => x=2

f''(x)=2/x^3+8 is >0 in x=2

hence the number is 2.