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PROJECT 5 - OPTIMIZATION paul vaz 1. Consider the function f ( x) x 3 4 x 2 4 x, for 0 x 4. (a) Locate the critical points. (It may be a good idea to view the graph of the function before calculating the critical points) (b) Find the global maximum and minimum on 0 x 4 . (See graph) 2. For some positive constant C, the temperature change, T, in a patient generated by a dose, D, of a drug is given by C D T ( )D 2 . 2 3 (a) What dosage maximizes the temperature change? (b) The sensitivity of the body, at dosage D, to the drug is defined as dT/dD. What dosage maximizes sensitivity? 3. A woman pulls a sled which, together with its load, has a mass of m kg. If her arm makes an angle of with her body (assumed vertical) and the coefficient of friction ( a positive constant) is , the least force, F, she must exert to move the sled is given by mg F . sin cos If = 0.15, find the maximum and minimum values of F for 0 / 2 . Give your answers as multiples of mg. Useful Commands: k:=expr; f:=diff(k,x); solve(f=0); subs(x=a,k); _____________________________________________________________ T:=(((C/2)-(D/3))*D^2); h:=diff(T,D); j:=factor(h); diff(j,D); _____________________________________________________________ F:=0.15/(sin(x)+0.15*cos(x)); F1:=diff(F,x); solve(F1=0); plot(F,x=0..Pi/2); subs(x=a,F); _____________________________________________________________