SOLUTION: Please answer this optimization problems 1:find the number/s in the interval I=[1/2,3] such that the sum of the number and it's reciprocal is a minimum. 2:A wire measuring 12 ft

Question 1135313: Please answer this optimization problems
1:find the number/s in the interval I=[1/2,3] such that the sum of the number and it's reciprocal is a minimum.
2:A wire measuring 12 ft long is cut into pieces. One piece is to be bent into a square and the other into a circle. How should the wire be cut so that the combined area is as large as possible?

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

1.  They ask you to find the minimum of the function

        f(x) = x + 

    in the interval  I = [1/2, 3].



    Take the derivative, equate it to zero and find the root:


    f'(x) = 1 - ;   f'(x) = 0  is the equation  1 -  = 0;

    as an equation, it is equivalent to   = 1,  which has only one root  x= 1  in the given interval.



    ANSWER.  x = 1.



To better illustrate the situation for you, I placed the plot below:



    


        Plot y = x + .

RELATED QUESTIONS
Help! I need help with a couple of problems. 1. Solve the inequality. Give the... (answered by edjones)

Hello can I please get help for these problems: Problem 1: Compute 𝑥^3 −... (answered by ikleyn)

find the number such that 2/3 of the number increased by 1 is... (answered by jorel555)

there is a two digit no. Such that sum of its digit is 6 while the product of digits (answered by ewatrrr)

I'm having problem soving the following problems. Please help. 2) Use the geometric... (answered by venugopalramana)

I would like to know if you could help me with this number problem. Thank you for your... (answered by ankor@dixie-net.com)

Please help me with this one... Number problems. Find two consecutive positive... (answered by checkley71)

Hey guys sorry for what i did earlier. I was able to answer 9 of it and i cant understand (answered by josgarithmetic)

Number problems. Find two consecutive positive integers such that the sum of their... (answered by checkley75)