Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let S be the sum of the number and its reciprocal. Write the objective function in terms of x. S(x) nothing The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation.) The number is 0.

--- Objective function

Interval =

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

Hence, the objective function is:

To get the the interval, we start by differentiating w.r.t x

Using first principle, this gives:

Equate S'(x) to 0 in order to solve for x

Subtract 1 from both sides

Multiply both sides by -1

Cross Multiply

Take positive square root of both sides because x is positive

Representing x using interval notation, we have

Interval =

To get the smallest sum, we substitute 1 for x in

Hence, the smallest sum is 2

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

i think 1: 2

step-by-step explanation: