Curve Sketching The cost function is described by the function f(x) shown below. The marginal cost (first derivative) and the derivative of the marginal cost is also given. [8] 3(x2 + 1) - 60r f'(x) = 180(x2 + 3) f(a) = x2 - 9 (2 - 9)2' f"(x) = (ac2 - 9)3 a) Graph the function by first determining the intervals of increase and decrease, the intervals of concavity and any local extrema or points of inflection.b) What asymptotes does this function have? What happens to the stock price over time?Geometric and Algebraic Vectors StrongStart decides to invest in a new robotic technology which makes possible mapping different types of territories. [6] a) Calculate the total displacement vector of the robot moving 2m SW and then 5m N30'E. Use triangle or parallelogram method. b) To push away an object it encounters in its path, the robot applies a force of 25 N at an angle of 40' and displaces the object 30 m. Determine the work done..Equations of Lines The robot starts its exploration at the point (2,1,2) and ends the exploration at the point (1,4,2). [4] a) Write the vector equation of the line describing the motion of the robot. b) Write this equation in parametric form