A. Use the definition of the derivative to find an equation of the tangent line to the graph of at the given point. 1. f(x)=2x2; (1,2) B. For each item, find the slope of the tangent line to y=f(x) at x = a. f ( x) = = , a = 0 1. C. In each item, sketch the region enclosed by the given curves, and find its area. Y= VX-I,x-V=1 7. D. A manufacturer packs sugar into plastic bag. Each bag is to hold 5 kilos of sugar. When the production is under control, each bag contains on the average 5 kilos. At one period, a sample of 17 bags was taken to check the process and was found to weigh 5.6 kilos with a standard deviation Of 0.75 kilos. Is the manufacturing process under control? Use a = 0.01. E. A college offers a course in Logic in either Filipino or English. Students argue that those who take the course in Filipino obtain higher average rating. The following are the result of the study conducted. Instruction Average Rating SD n Filipino 89 3 45 English 86 5 50 a) Verify the student's claim, if they are 95% confident about it. b) Test the hypothesis that there is in fact no difference between the average ratings of the two groups at 0.05 level of significance