For a dosage of $x$ cubic centimeters $(\mathrm{cc})$ of a certain drug, the resulting blood pressure $B$ is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs.
\[
B(x)=350 x^{2}-4200 x^{3}, 0 \leq x \leq 0.08
\]
The maximum is obtained for a dosage of (Round to two decimal places as needed.)

Step 1 ：First, we need to find the derivative of the function $B(x)$, which represents the rate of change of blood pressure with respect to dosage. This will help us find the maximum or minimum points of the function.

Step 2 ：The derivative of $B(x)$ is given by $B'(x) = 700x - 12600x^2$.

Step 3 ：To find the maximum or minimum points, we set the derivative equal to zero and solve for $x$. So, $700x - 12600x^2 = 0$.

Step 4 ：Factoring out $x$ gives $x(700 - 12600x) = 0$.

Step 5 ：Setting each factor equal to zero gives the solutions $x = 0$ and $x = \frac{700}{12600} = 0.05556$.

Step 6 ：We need to check the endpoints of the interval $[0, 0.08]$ and the critical point $x = 0.05556$ to determine where the maximum occurs.

Step 7 ：Substituting $x = 0$ into $B(x)$ gives $B(0) = 350(0)^2 - 4200(0)^3 = 0$.

Step 8 ：Substituting $x = 0.08$ into $B(x)$ gives $B(0.08) = 350(0.08)^2 - 4200(0.08)^3 = 1.792$.

Step 9 ：Substituting $x = 0.05556$ into $B(x)$ gives $B(0.05556) = 350(0.05556)^2 - 4200(0.05556)^3 = 0.607$.

Step 10 ：Comparing these values, we see that the maximum blood pressure occurs at a dosage of $0.08$ cubic centimeters, and the maximum blood pressure is $1.792$.

Step 11 ：Therefore, the maximum blood pressure is $1.792$ and it occurs at a dosage of $0.08$ cubic centimeters.