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

answer: f = 32.2m

step-by-step explanation: that is the answer

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.