Answer:
--- 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
<em>Using first principle, this gives:</em>
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
<em>Hence, the smallest sum is 2</em>