Question

Consider the function f(x)=x^2/x^2−9.

a.) f′(x) = -(18x/(x^2-9)^2)

b.) f(x) is increasing on the interval(s) ?

c.) f(x) is decreasing on the interval(s) ?

d.) f(x) has a local maximum at 0

e.) f′′(x) = (54(x^2+3)/(x^2-9)^3)

f.) f(x) is concave up on the interval(s) ?

g.) f(x) concave down on the interval(s) :(-3,3)

h.) f(x) has a horizontal asymptote y= 1

i.) f(x) has 2 vertical asymptotes x= -3,3

Can someone pleasee help me finish this problem.....

Answer 1

Ok first thing to do is find the critical numbers.. So set the first derivative equal to 0.

Answer 2

And solve for x