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Q7. (a) Use differential calculus to determine EACH of the following for the function

y = x³ - 3x² - 9x + 10

(i) the coordinates of the turning points; (7)

(ii) the nature of the turning points. (3)

(b) The area, A cm², of a pool of oil under a leaking sump is given by

A = t + t^2/16 where t is the time in minutes.

Calculate EACH of the following for the pool of oil after 20 minutes:

(i) the area; (2)

(ii) the rate the area is growing. (4)