One hour after x milligrams of a drug are given to a person, the change in body temperature T(x) (in degrees fahrenheit) is given by the functionT(x) = x2 (1 - (x/3)).Further, the rate T'(x) at which T changes with respect to the size of the dosage, x, is called the sensitivity to the body of the dosage. Find:a.) T'(1) = ?b.) T'(3) = ?c.) T'(6) = ?

Question
Asked Sep 23, 2019
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One hour after x milligrams of a drug are given to a person, the change in body temperature T(x) (in degrees fahrenheit) is given by the function

T(x) = x2 (1 - (x/3)).

Further, the rate T'(x) at which T changes with respect to the size of the dosage, x, is called the sensitivity to the body of the dosage. Find:

a.) T'(1) = ?

b.) T'(3) = ?

c.) T'(6) = ?

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Expert Answer

Step 1

Calculation:

Differentiate the given function T(x) = x2(1 – (x/3)) with respect to x as follows.

T’(x) = 2x – x2.

Compute the value of T’(x) at x = 1, x = 3 and x = 6 as follows.

T’(1) = 2(1) – 12

            = 1

T&...

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