toxicsugar22
  • toxicsugar22
">A doctor who is treated a heart patient wants to presicribe medication to lowere the patients blood pressure. The body's reaction to this medication is a function of the dose admininistered. If the patient takes x milliters of the medication, his blood pressure should decrease by r=f(x) points where f(x)=3x^2-1/3x^3 How much should the patients blood pressure drop if he takes 2 milliieters of medication which i got 9.333 What is the maximum drop in blood pressure that can be achieved with this medication ?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
For the first part, just substitute 2 for x and solve. For the second part, derive and set equal to zero, solve.
toxicsugar22
  • toxicsugar22
sii it would be 3(2)^2-1/3(2)^3=0
toxicsugar22
  • toxicsugar22
so it would be like 3(2)^2-1/3(2)^3=0

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anonymous
  • anonymous
They're separate parts. First you solve for x=2 and then set the derivative to zero and solve to find the dosage that gives the maximum.
anonymous
  • anonymous
Once you find the dosage, you can out that in the original equation to ge the maximum drop in pressure.
toxicsugar22
  • toxicsugar22
can u show please
toxicsugar22
  • toxicsugar22
please
toxicsugar22
  • toxicsugar22
like how do u solve for x=2
toxicsugar22
  • toxicsugar22
r u there
anonymous
  • anonymous
Sure. \[F(2)=(3(2^{2}))\div(3(2^{3})) = 12/24 = 1/2\] Which gives us the points that he dropped by taking 2 mL of medication. This is how Hurons the max: \[F'(x)=[6x](3x ^{3}) - (3x ^{2}-1)[9x2] \div (3x ^{3})^{2}\] Setting that equal to zero, we get x=+-1. We know it can't be negative 1 because you can't give negative medicine, so plug in one and solve to get 2/3.
toxicsugar22
  • toxicsugar22
plug in 1 where
toxicsugar22
  • toxicsugar22
for what values of x make sencefor this function
toxicsugar22
  • toxicsugar22
and use interval notation
toxicsugar22
  • toxicsugar22
Find the first three terms in asending powers. 1-2x^2-x^4)(4+x^2-2x^4)

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