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Find a number in the closed interval [1/2,3/2] such that the sum of the number and its reciprocal is a.)as small as possible

Question

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## Answers ( No )

Let’s assume that number as x

so,

the sum of the number and its reciprocal is

Firstly, we will find derivative

now, we can set it to 0

and then we can solve for x

Since, only x=1 lies on [1/2,3/2]

so, we will consider only x=1

now, we can plug end values and x=1 into S

At x=1/2:we can plug x=1/2

At x=1:we can plug x=1

At x=3/2:we can plug x=3/2

(a)Smallest value:The smallest value among them

So, a number is 1……….Answer(b)Largest value:The largest value among them

So, a number is ……..Answer