Answer the following questions using the given equation

Question

f(x) = x³/(х²-3)

f’(x) = x⁴- 9х²/(x²-3)³

f"(x) = 6x(x² + 9)/(x² -3)³

Answer the following:

(a) What's the domain of the function f(x) ?

(b) Find all horizontal and vertical asymptotes of f(x).

(c) Find all critical points of f(x) in the domain. Find the intervals in the domain where f(x) is increasing and the intervals in the domain where f(x) is decreasing. Then find all local max and local min of f(x) in the domain.

(d) Find where f(x) is concave up and where it is concave down. Then find all inflection points of f(x)

(e) Using the previous parts, sketch the graph of f(x)

Answer 1

desmos.com/calculator/sc84tkvvc6

In the above graph enable both f'(x) and g(x) to confirm correctness for first derivative.

Similarly for f''(x) and h(x).