Respuesta :
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
