The formula \( D=50 e^{-0.4 h} \) can be used to find the number of milligrams \( D \) of a certain drug that is in a patient's bloodstream \( h \) hours after the drug was administered. When the number of milligrams reaches 3 , the drug is to be administered again. What is the time between injections? The time between injections is (Round to two decimal places as needed.).

Find \( (A) f^{\prime}(x) \), (B) the partition numbers for \( f^{\prime} \), and \( (C) \) the critical numbers of \( f \). \( f(x)=x^{3}-12 x-8 \) (A) \( f^{\prime}(x)=\square \) (B) Find the partition numbers for \( f^{\prime} \). Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. The partition pumber(s) is/are \( x=\square \). (Use a comma to separate answers as needed.) B. There are no partition numbers. (C) Find the critical numbers for \( f \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical number(s) is/are \( x=\square \). (Use a comma to separate answers as needed.)

1) \( \int_{8}^{\frac{\text { III }}{\frac{\pi}{2}}} x \cdot c \)

9.- Calcula la derivada de la función * \( y=\left(x^{2}+b^{2}\right)^{4} \) \( \begin{array}{ll}\text { A) } \frac{d y}{d x} 8 x\left(x^{2}+b^{2}\right)^{5} & \text { B) } \frac{d y}{d x} 8 x^{2}\left(x^{2}+b\right)^{3} \\ \text { C) } \frac{d y}{d x} 8 x\left(x^{2}+b^{2}\right)^{3} & \text { D) } \frac{d y}{d x} 8\left(x^{2}+b^{2}\right)^{3}\end{array} \)

\( \int \frac { 3 / \sqrt { a ^ { 3 } y ^ { 4 } } x d x } { 4 / 3 a ^ { 2 } b ^ { 3 } x ^ { 2 } + 6 } \)

\( \lim _ { x \rightarrow \infty } ( \frac { 3 x + 1 } { 3 x - 5 } ) ^ { \frac { 3 x ^ { 5 } + 4 x - 3 } { ( 2 x - 1 ) ^ { 2 } ( x + 2 ) ^ { 2 } } } \)