Use the given function and its derivatives to answer the questions. Then sketch the graph.

f(x)=(x²+36) / x

f'(x)=(x6)(x+6) / x²

f''(x)=72 / x³

(a) State the domain off(x).

(Enter your answer using interval notation.)

(b) State they-interceptoff(x).

(If an answer does not exist, enter DNE.)

(c) State the open interval(s) wheref(x)

is increasing. (Enter your answer using interval notation.)

(d) State the open interval(s) wheref(x)

is decreasing. (Enter your answer using interval notation.)

(e) State any points wheref(x)

has a local maximum. (If an answer does not exist, enter DNE.)

(x,y) =

(f) State any points wheref(x)

has a local minimum. (If an answer does not exist, enter DNE.)

(x,y) =

(g) State the open interval(s) wheref(x)

is concave up. (Enter your answer using interval notation.)

(h) State the open interval(s) wheref(x)

is concave down. (Enter your answer using interval notation.)

(i) State any inflection points off(x).

(If an answer does not exist, enter DNE.)

(x,y) =

(j) State any vertical asymptotes off(x).

(Enter your answer as a comma-separated list of equations. If an answer does not exist, enter DNE.)

(k) State any horizontal or oblique (slant) asymptotes off(x).

(Enter your answer as a comma-separated list of equations. If an answer does not exist, enter DNE.)

(l) Sketch the graph off(x).

This is a super beefy homework problem. It is also one of the only two he assigned. I hope this isn't too bad. Thanks an advance.