SOLUTION: Calculus Problem, Applied Optimization Find a positive number for which the sum of its reciprocaland four times its square is the smallest number.

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Question 379613: Calculus Problem, Applied Optimization
Find a positive number for which the sum of its reciprocaland four times its square is the smallest number.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let N be the number.
f%28N%29=1%2FN%2B4N%5E2
graph%28300%2C300%2C-1%2C9%2C-1%2C9%2C0%2C1%2Fx%2B4x%5E2%29
Take the derivative of f(N) and set it equal to zero.
df%2FdN=-1%2FN%5E2%2B8N
1%2FN%5E2=8N
N%5E3=1%2F8
highlight%28N=1%2F2%29