Differentiation and Reccurence Q 6 - 10

6. For the curve

find the equation of the tangent to y at

7. A crop is sprayed weekly with Killall weedkiller. This weedkiller kills 80% of all weeds but 30 new weeds grow each week. A different weedkiller is used on a similar crop and this weedkiller, called Killem, destroys 70% of weeds with 25 new weeds growing each week.

Which weedkiller is the most effective in the long run.

8. Sketch and annotate fully the curve

9. When a ship is travelling at a speed of v km per hour, its rate of consumption of fuel is tonnes per hour.

a) Prove that the total amount of fuel used on a voyage of 5000km at a speed of v km/h is tonnes.

b) Hence find the speed, which gives the greatest fuel economy for this voyage, and find the amount of fuel then used.

10. Below is the graph of . Sketch the graph of and find the maximum and the minimum value of in the interval