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

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

i hope this is what you were looking for.

see attached graph

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: