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f(x)= 2x+3+(18/x-4)

differantiating it, we get,

2-18/x^2=0

2x^2= 18

x^2= 9

x= 3, -3

I have trying to post part 2. The file is not getting uploaded due to some technical glitch.

By the time it gets fixed, let me have the opportunity to ask you whether you are acquainted with the "wavy curve method" of solving inequalities or not. This is the most "basic and easy to understand" method. You may ping me, in case you want to learn it. You will be able to solve all kinds of inequalities you will encounter in this chapter or elsewhere.

I have used this technique to solve the last part of the question.  You must know, how to solve inequality to solve the questions of increasing and decreasing function.

Dear shekharrrrn, I am afraid that your derivative is not correct... If you don't want to convert 2x+3 into a fraction and differentiate instantly (as you did), you get

df/dx= 2-18/(x-4)^2, since 18/(x-4)= 18(x-4)^(-1)= -18(x-4)^(-2)

because x^n=nx^(n-1). If you simplify now you will get the same answer as me, x<1 or x>7.

For a function to be increasing, the tangent of a function must be greater than 0.

In other words it means the differentiation of the function should be greater than 0.

hence

d/dx (f)= d/dx (2x+3 +(18/x - 4 )) >0

2 -18/x^2 >0

18/x^2 <2

x^2 >18/2

x^2 >9

it means either x>3 or x<-3

so solution is x belongs to  (-infinity,-3) +( 3,infinity)

I ve got the answer, just give me a couple of hours because I am about to start a lesson. I will write down everything with every single detail that is required. You will see that it is not hard. :-)