# How do you use the first and second derivatives to sketch # f(x)=(x+2)/(x-3)#?

##### 1 Answer

Jan 8, 2017

graph{(x+2)/(x-3) [-15.58, 24.42, -8.16, 11.84]}

#### Explanation:

We can now analyse the behaviour of the derivatives to sketch the function:

(1)

#f'(x) < 0# everywhere in its domain#RR -{3}# , so#f(x)# is strictly decreasing and has no local extrema.(2) for

#x < 3# ,#f''(x) < 0# so#f(x)# is concave down in#(-oo,3)# (3) for

#x > 3# ,#f''(x) > 0# so#f(x)# is concave up in#(3,+oo)#