Answer Happy

Please solve the a and b sections of Q15 down below, it’s
urgent. The answers to the questions are below the question. I need
the solutions for the questions in great detail. I will upvote your
answer .
Q15. Let f(x) = x² - 18x². (a) Find the domain of f, and, find x-intercepts and y-intercepts of the graph of f. (Ans.: Domain: (-∞, ∞), Intercepts: (0,0), (-3√(2),0) and (3√(2), 0)) (b) Find the critical values of f. Determine intervals on which the function f is increasing and intervals on which the function is decreasing. Determine relative extrema (maximum and minimum) of f, if any. (Ans.: CVs: x = 0, x = −3 and x = 3, Increasing: (-3,0) and (3, ∞), Decreasing: (-∞, -3) and (0, 3), Rel. max. at: x = 0, Rel. min. at: x = -3 and x = 3) (c) Determine intervals on which the function f is concave up and intervals on which the function is concave down. Find the inflection points, if any. (Ans.: Concave down: (-√3, √√3), Concave up: (-∞, -√3) and (√√3, ∞), Inflection Points at: x = -√3 and x = √3) (d) Sketch the graph of f including intercepts, relative extrema and inflection points.