5. If the radius changes at a rate of 3.0 cmfmin, at what rate is the sphere's surface area changing when the radius is 5 cm? [2 marks] 6. Find 3: by differentiating implicitly. Express your answer in terms of x and y a) x2y+ 2x3 = b) Jr+2y\"3y+4-:r2 = 5 [2x2 marks] 7. A biologist wants to make a rectangular cage along the outside of the lab and has enough materials for 20 m of fencing. Clnl},r 3 sides must be fenced, as the wall of the lab will form the fourth side. What are the dimensions of the rectangle the biologist should use so the maximum area is enclosed? [3 marks] 8. Find two positive numbers with product 100 such that the sum of one number and twice the second number is a minimum. [2 marks] 9. Alex needs to fence in 300 sq. yds., with one wall being made of stone which costs $24 per yard, and the other three sides being wire mesh which costs $8 per yard. What dimensions will minimize cost? [ Zmarks]