22. A stone is launched vertically upward from a cliff 448 ft above the ground at a speed of \( 48 \mathrm{ft} / \mathrm{s} \). Its height above the ground t seconds after the launch is given by \( \mathrm{s}=-16 \mathrm{t}^{2}+48 \mathrm{t}+448 \) for \( 0 \leq \mathrm{t} \leq 7 \). When does the stone reach its maximum height? Find the derivative of s . \( \mathrm{s}^{\prime}=\square \) The stone reaches its maximum height at (Simplify your answer.)

19. Find critical points of \( f(x, y, z)=x y+y z \) with constraints \( x^{2}+y^{2}=8 \) dan \( y z=8 \)

\( \left. \begin{array} { l l } { y ^ { \prime } - y = 0 } & { y ( 0 ) = 0 } \\ { } & { y ^ { \prime } ( 0 ) = 1 } \\ { } & { y ^ { \prime \prime } ( 0 ) = 0 } \\ { } & { y ^ { \prime \prime } ( 0 ) = 0 } \end{array} \right. \)

3. Hitung luas daerah yang dibatasi oleh kurva \( y=x^{2} \) dan \( y=4 x-x^{2} \)

Berilgan qatorlarni absolyut va shartli yaqinlashishga tekshiring. \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+1) \ln (n+1)} \]

2. Hitung nilai integral berikut dengan batas-batas yang diberikan: \[ \int_{1}^{3}\left(2 x^{3}-4 x^{2}+x\right) d x \]