Sample+problem

Sorry - the question is somehow lost here!

Average rate of change = slope = change in f(x) / change in x

= [(3^4) - 5(3)] - [(0^4) - 5(0)] / (3-0) = (66 - 0) / (3 - 0) = 66/3 = C) 22

-Dan G This is an excellent example, but it should really go under the "related rates" section! Actually now I see that it IS under the related rates section....somehow this page was linked twice! Sorry -- it is still a good page! (Ms. Sweeney) Sophia Hirsch A Circle is inscribed in a square. The circumferance of the circle is increasing at a constant rate of 6 in/sec. As the circle expands, the square expands to maintain the condition of tangency. a) find the rate at which the perimeter of the square is increasing. Indicate units of measure.

dc/dt = 6 in/sec C = 2 pi r dc/dt = 2 pi dr/dt 6 = 2 pi dr/dt dr/dt = .9549 in/sec

s = 2r P= 4s P = 2(4r) P = 8r dP/dt = 8 dr/dt dP/dt = 8 (.9549) dP/dt = 7.639 in^2/sec

b) at the instant when the area enclosed is 25pi square inches, find the rate of increase in the area enclosed between the circle and the square. Indicate units of measure.

Area = 25 pi Area = pi r^2 25 pi = pi r^2 r = 5

A= Area square - Area circle A= s^2 - pi r^2 A = (2r)^2 - pi r^2 A = 4r^2 - pi r^2 dA/dt = 8r dr/dt - 2 pi r dr/dt dA/dt = (8)(5) - 2 pi (5)