The question is to find where the graph is increasing or decreasing.
The original function is $f(x)={(x^2+2x-48)}/{x^2}$
I know I need to find the prime of this function and I think it is this after using the quotient rule:
$2(-x^2-x+49)/x^3$
Finally, in order to draw a graph I need to find the points on the x axis that are either undefined and/or the slope equals 0.
Immediately I know that 0 is an undefined point because it makes the prime graph undefined.
It's when I take the numerator and set it equal to 0 that trips me up.
$2(-x^2-x+49)=0$
$-x^2-x+49=0$
$(x)(x)=0$
I'm guessing I did something wrong finding this prime because the answers are all including the number 48. I'm stumped because I've been at this question for about 1 hour.
Thanks!