Question 1 Compute critical points, concavity at those points, points of inflection for the following functions. Then, find the most appropriate graph for each function based on the quantities you computed. y = 5x' + 7x - 2 Local minimum at r = y" at this point = Graph: Choose one graph fr Enter a decimal number with more than 4 significant digits if not an integer. y = - 5x3 + 3x2 + 6x - 2 Local minimum at c = y" at this point = Local maximum at = = y" at this point = Point of inflection at r = y" at this point = Graph: Choose one graph from below. y = 4x + x - 18x' + 81 [Hint] Smallest local minimum at x = y" at this point = Largest local maximum at = = y" at this point = Point of inflection between the above 2 points at c = y" at this point of inflection = Graph: Choose one graph from below.Question 2 Sketch the graph of y = (x -2)e-(-2) /3 by computing the following quantities. [Hint] *x increases from left to right. Express large or small numbers, e.g., 1.2345 x 10-42 as 1. 2345e-42. Extremum r-intercept Extremum 12 y 0 y 0 O Check your sketch using a graphing tool such as desmos calculator. Check answers!Question 3 At a price of $23 a chemical company can sell 800 vials of a certain compound that cost $15 to manufacture. For every dollar that the company lowers the price, the number sold can be increased by 400. What selling price will maximize the total profit? Sketch the graph of the profit versus the selling price, and check if your result makes sense. [Hint] Selling price = $ Check answers!Question 4 Suppose you have identical tiles of dimensions r m by ym of a fixed area of 30 m . Find r and y that will minimize the perimeter of the rectangle region covered by 7 tiles in the r-direection and 2 tiles in the y- direction, i.e., the length of the perimeter is 2(7x + 2y). Check answers!Question 5 Let us derive the derivative formula for In a using implicit derivative. Let y = Inc [Eq.1] Expressing it in the exponential form, we have [Eq.2] Differentiating Eq.2 with respect to x gives y' in terms of y [Eq.3] Substituting Eq.2 in Eq.3 we have y' in terms of a as [Eq.3] Check answers!