Unit 2: Derivatives MCV4U Review Questions...

Question 1:

6. Determine the values of a and b for the function f(x) = ax + 3bx - 4x - 29 given that f(-2) = 11 and the slope of the tangent to the curve at x = -1 is my = -3. (6)Use the Chain Rule (Leibniz Notation) for d) and the Chain Rule (Generalized Power Rule) for e) below. 14 d) y = V/2x3+7 12 e) g(x) =-2(1-3x) 15 3x4 13 f) 9 ( x ) = 6x-11 Quotient RuleDetermine the coordinates of the point on the graph of f (x) = (V10x + 8) where the tangent line is parallel to the line y = -24x + 11. (5)\f(2x-+)' (2x-7) 5. Determine the coordinates of the point on the graph of /(x) = (V20x -28) where the tangent line is d'cularyto the line y = -=x + 5. (6)\fstore sells 360 stainless steel thermal travel mugs per month of a price of $36 each. A market survey indicates that for each $2.75 decrease in price, sales will increase by 44 travel mugs. " ) Determine on 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) letermine the demand function, p(x]. (2)c) Determine the revenue function, R(x). (1)d) The total cost, C, in dollars, of producing * travel mugs is C(x) = 0.0022x" + 0.95x + 3900. Determine the marginal profit when 400 mugs are sold. (3)7. The position of a particle moving along a straight line is modelled by the function s(t) = -2+3 + 12t2 + 11, where displacement, s, is in metres, and time, t. is in seconds: and t 2 0. a) Use differential calculus to determine the velocity at 4.4 seconds. Is the particle moving forwards or backwards at this time? (3)b) Determine when the velocity is 0 m/s. (2)