Consider the function :[1,∞)→Rgivenbytheformulay=x3+2.

Question

(a) Show that though the function is increasing at an increasing rate, the change in x required to double the value of the function is not constant.

(b) Make a table of values for constant changes in x, and investigate whether or not the property ∆y ∝ y is satisfied.

Answer 1

heck, the answer to the 2nd part provides the answer to the first part:

x y ∆y
1 3
2 10 7
3 29 19
4 66 37
5 127 61
6 218 91

as you can see, x has to increase less and less for y to double.

Answer 2

Thank you very much Steve..