Q1. Suppose the derivative of a function f(x) with domain D = is given as

f(x) = (8 + x)2(5 x) x2 + 3

(a)Find the two critical values. Separate your answers with a comma. (b)Find the interval where f is decreasing. The interval is of the form (a,b). Enter the values of a and b (in that order) into the answer box below, separated with a comma. (c)Find the x-coordinate of the relative maximum of f (if any). If there is no relative maximum, then enter DNE. (d)Find the x-coordinate of the relative minimum of f (if any). If there is no relative minimum, then enter DNE.

Q2. a)Find the equation of the line that is tangent to the graph of the function f(x) = ln(6x + 5) at the point (0,ln5). (b)Find the equation of the line through the point (6,5) and parallel to the line 6x + 3y = 9.

Put your answers in the form y = mx + b, but do not include the 'y = ' part in the answer box.

Q3. Find the equation of the line that is tangent to the graph of the function f(x) = ln(6x + 5) at the point (0,ln5). (b)Find the equation of the line through the point (6,5) and parallel to the line 6x + 3y = 9.

Put your answers in the form y = mx + b, but do not include the 'y = ' part in the answer box.

Q4.

Your friend needs to save $4500 to go on a trip to Argentina in 7 years and the annual interest rate is 4%. How much should she invest now if the interest rate is compounded:

(a)Continuously? (b)Semiannually?