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

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.