Follow the curve sketching algorithm and provide detailed work (showing every step) and sketch for the following functions: (Your work must include non derivative analysis, 1st derivative
analysis and second derivative analysis and using proper notations)
Note: For part a, your critical points and points of inflection can be decimal numbers.
For part b, ALL important points must be in exact form.
a)
f(x) = (x - 1)(2x2 - 5x - 12)
(10 Marks Application and 4 Marks Communication)
1- x2
f(x) =
1 + x2
b)
(10 Marks Application and 4 Marks Communication)

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?