Posted by **alan** on Friday, May 20, 2011 at 4:38am.

(a)(i)use the composite rule to differentiate the function f(x)=(x^2-6x+23)^(3/2).

(ii)use the composite rule and your answer to part (a)(i) to show that the function g(x)=(x-2)/(x^2-6x+23)^(3/2) has derivative g'(x)=(5+9x-2x^2)/(x^2-6x+23)^(5/2).

(iii)find any staionary points of the funtion g(x) defined in part (a)(ii) and use the first derivative test to classify each stationary point as a local maximum or local minimum og g(x).

(iv)using your answers to parts (a)(ii) and (a)(iii) find the area bounded above by the graph of y=(100(2x+1)(5-x))/(x^2-6x+23)^(5/2) and below by the x-axis. give your answer to four significant figures.

(b)(i)using your answer to part (a)(i) find the greneral solution of the differential eqution dy/dx=2/27(x-3)√((x^2-6x+23)/y) (y>0) giving the solution in implicit form.

(ii)find the particular solution of the differntial equation in part (b)(i) for which y=2 when x=1 and the give this particular solution in explicit form.