maths
posted by alan .
(a)(i)use the composite rule to differentiate the function f(x)=(x^26x+23)^(3/2).
(ii)use the composite rule and your answer to part (a)(i) to show that the function g(x)=(x2)/(x^26x+23)^(3/2) has derivative g'(x)=(5+9x2x^2)/(x^26x+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)(5x))/(x^26x+23)^(5/2) and below by the xaxis. 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(x3)√((x^26x+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.
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