maths

posted by .

(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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) …
  2. Calculus

    Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that …
  3. maths

    differentiate the following function using the composite rule h(x)=e^x(4-x)/6
  4. calculus

    Please can someone help. I need to use the composite rule to differentiate the function f(x)=(x^2-6x+23)^3/2. Any help would be greatly appreciated.
  5. Math - Domain of Composite function

    Find the domain of the composite function f ₒ g . Please show all of your work. f(x) = √x; g(x) = 2x + 12
  6. cal3

    Using the chain rule, find the min and max points and their values of the composite function defined by: z= x^2 + y^2, x=sin(2t), y=cos(t)
  7. applied calculus

    1. Consider the function y = xx (for x> 0). a) Why does the derivative rule for xn not apply?
  8. Math22

    1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y= (g(x), f(u)) = 2. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) …
  9. Calculus

    What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like?
  10. Calculus

    What would an example of a logarithmic function that contains a radical within it and a quotient within it where you would need to use chain rule and quotient rule to take derivative look like?

More Similar Questions