3) Given f(x) = 3-23 and its first and second derivatives f'(x) = - 12(3-x²) (x²+3)2 and f"(x) = 24x(9-x²) respectively.

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3 Given F X 3 23 And Its First And Second Derivatives F X 12 3 X X 3 2 And F X 24x 9 X Respectively 1 (35.47 KiB) Viewed 13 times

3) Given f(x) = 3-23 and its first and second derivatives f'(x) = - 12(3-x²) (x²+3)2 and f"(x) = 24x(9-x²) respectively. (x²+3)3 [3+3=6 marks] a) Find the critical numbers and the (x, y) coordinates of any local minima or maxima of f(x). b) Find the intervals of concavity and the (x, y) coordinates of any inflection points. 4) A company selling widgets has found that the number of items sold q depends upon the price p at which they're sold, according to the equation q = 10000 5) Sketch the graph of f(x) from the given information below: a) Domain: (-00, 1) U (1,00) b) Intercepts: x-intercept=-1 and y-intercept=-1 c) Asymptotes: Horizontal y=1 and vertical x=1 d) Decreasing on: (-00, 1) U (1,00) e) No Relative extrema f) Concavity: Downward on (-00, 1) upward on (1,00) g) No Inflection points √5p+1 Due to inflation and increasing health benefit costs, the company has been increasing the price by $3 per month. Find the rate at which the revenue is changing when the company is selling widgets at $180 each. [6 marks] [4 marks]