A7. (a) Which of the following statements is true? Select one of the options i.- iv. dy' The derivative of the function Y = 4x6 - 3x3 + 7x - 5 is equal to dx, i. 24x6 -9x3 + 7 ii. 24x5 - 9x2 + 7 ii. 24x5 - 9x3 + 7 iv. None of the above Given that the demand function is p = 42 - 3q , where q represents the output level and p is the price, write down an expression for the total revenue (R) function in terms of q. (b) i. Find the output level which maximises the total revenue function. Note that you need to clearly show that this output level leads to a maximum. ii.

4. Let G represent the number of gallons of gasoline left in a car’s tank after it has been driven m miles from a filling station where it was last filled. The table below gives se- lected values of these quantities:   (a)  What kind of function is G = G(m)? How can you tell? (b) Determine the slope of the line that connects the first point (40, 11) to the last point (200, 3) from the table above. Interpret what this number tells us about how this car uses gasoline. (c)  Find the y-intercept of the line that connects the first point (40, 11) to the last point (200, 3) from the table above. Interpret what this number tells us about how this car uses gasoline.

1. A liquid starts at an initial temperature of 175 C and cools down in a room held at a constant temperature of 16 C. It's temperature can be modeled, as a function of time cooling, by the equation y=a(b) +c. which of the following statements is true? (1) a=159 andc=16 (3) a=175 andc=16 (2) a=16 andc=159 (4) a=16 and c=175 14

Find the slope of the graph of the function at the given value. f(x)=-3x²+ Select one: O b. 7 O a. f'(2)= x O e. when x = 2 f'(2)=- c. f'(2) = - d. f'(2)= 55 8 39 4 55 39 4 55 f'(2)= 4 X Incorrect