7) Gravel is being dumped from a conveyor belt at a rate of 25 t3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Give your answer correct to three decimal places.
8) If f(x) + x^2[f(x)]^3 = 30 and f(1) = 3, find f '(1).
Re-write this as y + x^2 y^3 = 30. Use implicit differentiation to get dy/dx (the re-write makes it easier to see how to do this. The technique ought to be in your class notes or textbook if you're being given questions on it).
Substitute y = 3 and x = 1 to get the required value of dy/dx.
If you need more help please state what you've done and where you get stuck.