How do I find if this equation is increasingdecreasing And t

How do I find if this equation is increasing/decreasing. And then how do i identify local extreme values. Any help is greatly appreciated!!!

Solution

f(x) =only by taking derivative : f\'(x) = (x-7)[2x] - [x*x -48] / (x-7)^2 : 2x*x - 14x - x*x + 48 / (x-7)^2 : x*x - 14x + 48/(x-7)^2 > 0 for increasing interval x = 14 +- 2 / 2 : 8 , 6 increasing for (-infinity , 6] U [8 , infinity) and decreasing on [6,7) U (7,8] so c) is the correct option !!! check values at x = -infinity , 6, 7 ,8, infinity x = 6 is a local maxima , x =8 is a local minima this can be done by second serivative test , if second derivative comes out -ve at x=6 ,, then maxima otherwise minima , similarly at x=8 at x -> 7- : -infinity at x-> 7+ : +infinity absolte maxima = + infintiy absolute minima : - infinity B) is the correct option !!!