Given the differential equation \( y' = 2y - x \), draw a rough sketch of its slope field at points (-1,0) and (0,1).

10.- Calcula la derivada de la función * \( y=12 x^{4}+5 x^{3}-3 x^{2}+5 \) \( \begin{array}{ll}\text { A) } \frac{d y}{d x} 48 x^{3}+15 x^{2}-6 x & \text { B) } \frac{d y}{d x} 48 x^{4}+15 x^{2}-6 x \\ \text { C) } \frac{d y}{d x} 48 x^{3}+15 x^{2}+6 x & \text { D) } \frac{d y}{d x} 48 x^{2}+15 x^{2}-6 x\end{array} \)

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

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

Integrate as indicated. Assume \( \mathrm{g}(\mathrm{x})>0 \) whenever \( \ln g(\mathrm{x}) \) is involved. \( \int \frac{8 \mathrm{x}}{4 \mathrm{x}^{2}+1} \mathrm{dx} \) \( \int \frac{8 \mathrm{x}}{4 \mathrm{x}^{2}+1} \mathrm{dx}= \)

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.)