Please show the answer step-by-step that I could understand clearly.

Thanks!

Question 5: [19 points] Given the following function and its first and second derivatives. Answer to the following questions. Show your work. f (x) =- 3x2 -12x x2 - 2 f' (x) = (x2 - 2)2 and f"(x) = 36x-+ 24 (x2 - 2)3 a) [1] Find the domain of f : b) [1 ] Is f even, odd or none? : c) [1] Find the Coordinates of the critical point(s): d) [1] Find the vertical asymptote(s): e) [1] Find the horizontal asymptote(s). f) [2] Find the open interval(s) where f is increasing. g) [2] Find the open interval(s) where f is decreasing. h) [1] Find the local maximum. i) [1] Find the local minimum. j) [2] Find the open interval(s) where f is concave upward. k) [1] Find the open interval(s) where f is concave downward 1) [1] Find the coordinates of any inflection point(s). m) [4] Sketch the graph of f by labelling the key points (maximum, minimum, intercepts...)