Hi this is a practice test for grade 12 MCV4U Unit #2 test.

Do you mind clearly showing the steps to help me out? I'm confused on derivatives.

MCV4U Unit #2 Test Part 2 Include units in your answers for the following rate of change problems. 7. The position of a particle moving along a straight line is modelled by the function s(t) = 13 - 5t? - 15t + 11. where displacement, s, is in metres, and time, t. is in seconds; and O s t $ 7. a) Determine the velocity at 2.9 seconds. (2) b) Determine the time(s) when the particle is at rest. (2) c) Determine when the acceleration is 2.4 m/s. (2) Given the graph to the right of a particle's displacement, s(t), where x E [d, Do) (9, B ) a) In which interval(s) is the velocity negative? (1) (d, 0 ) ( f , 0 ) (h b) In which interval(s) is the acceleration positive? (1) (e, A)A store sells 180 stainless steel thermal travel mugs per month at a price of $24.25 each. A market survey indicates that for each $2.25 increase in price, sales will decrease by 12 travel mugs. 4) Determine an equation for the price as a function of n, p(n), and an equation for the number of mugs sold, x(n), as a function of n, where n represents the amount of increase/decrease. (1) b) Determine the demand function, p(x). (2) Determine the revenue function, R(x). (1) d) The total cost, C, in dollars, of producing x travel mugs is C(x) = -0.099x + 7.7x + 3333. Determine the marginal profit when 260 mugs are sold. (3) 10. Differentiate the following functions. Final answers should have no negative exponents and should be in fully factored/simplified form. (15 marks) a) y = (VBu) , and u = -x4+7b) P(x) = (5 - 2x3)8(3x* + 2)10 (2x2+1)6 c) Q(x) = V/3x-4