please show steps/work clearly

Sketch the graph of the rational function 23;2 x2 1 f(x) = by determining the answers to the following parts. You must show calculations for each step and your graph must be derived from your work (meaning, do not graph using Desmos). (A) State the domain in interval notation. [1 mark]. (B) Determine any intercepts, written as points [2 marks]. (C) State the equations of any vertical asymptotes and use one-sided limits to determine the local behavior around the asymptotes. [5 marks]. (D) Use limits at infinity to calculate the equation of any horizontal asymptotes. [2 marks]. (E) Use the first derivative to determine the intervals where the function increases and decreases. [6 marks]. (F) Using the results from your sign chart in (E), list any local extrema as points. [1 mark]. (G) Using the second derivative, determine the intervals where the function is concave up and down. [6 marks]. (H) List any inflection points. [1 mark]. (I) Graph the function. Make sure you label everything you found in the steps above. [3 marks]. Exercise 1 (Based on Section 4.10}. [3 marks]. Calculate the antiderivative, F (x), of the function f(x) = 2x + 6 cos x, where F05) = x2 + 2. Exercise 2 (Based on Section 4.2). [2 marks]. Calculate the differential of y = x2 5x 6, and evaluate it for x = 2with dx = 0.1