Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition? 

Hi, I think there must be an error in this problem. I read "Show that a dose between 8 and 12 units satisfies this requirement" as "Show that every dose between 8 and 12 units satisfies this requirement", and this is not true. You can check that if x is 11 then R is larger than 21. If the sentence should be read "Show that there is a dose between 8 and 12 units satisfies this requirement" then this is true. Again you can check that if the dose is 9 then R is less than 21. If this second interpretation is correct than what is the greatest value of x that results in R not exceeding 21? I know that the functions lnx and x are increasing so R is increasing. Hence the value of x you want is the one that satisfies
Now you need to approximate x to 5 decimal places. Harley 

