For a dosage of x cubic centimeters​ (cc) of a certain​ drug, assume that the resulting blood pressure B is approximated by B (x) = 0.06 x^2 - 0.3 x^3 . Find the dosage at which the resulting blood pressure is maximized. Round to two decimal places.

Accepted Solution

Answer:The number of dosage is 0.13.Step-by-step explanation:Here, the given function that represents the blood pressure,[tex]B(x)=0.06x^2 - 0.3x^3[/tex]Where, x is the number of dosage in cubic centimeters​,Differentiating the above function with respect to x,[tex]B'(x)=0.12x-0.9x^2[/tex]For maximum or minimum blood pressure,[tex]B'(x)=0[/tex][tex]0.12x-0.9x^2=0[/tex][tex]-0.9x^2=-0.12x[/tex][tex]x=\frac{0.12}{0.9}=\frac{2}{15}[/tex]Again differentiating B'(x) with respect to x,[tex]B''(x)=0.12-1.8x[/tex]Since, at x = 2/15,[tex]B''(\frac{2}{15})=0.12-1.8(\frac{2}{15})=0.12-0.24=-0.12=\text{Negative value}[/tex]So, at x = 2/15 the value of B(x) is maximum,Hence, the number of dosage at which the resulting blood pressure is maximized = 2/15 = 0.133333333333 ≈ 0.13