Between 0 degrees Celsius and 30 degrees Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula \( V=999.87-0.06426 T+0.0085043 T^{2}-0.0000679 T^{3} \) Find the temperature at which water has its maximum density. Temperature \( = \)

(b) \( f(x)=-x^{6}-8 x^{5}-7 x^{4}+6 x^{2} \) Falls to the left and rises to the right Rises to the left and falls to the right Falls to the left and falls to the right

derivates \( y=\frac{1+x^{3}}{1-x^{3}} \)

(f) \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}{1-\tan x} \)

CHECKING COMPREMENSION (press pause for more time) Find the volume of the solid of revolution that results from rotating \( y=x^{2}+3 \) around the \( x \) axis, over the interval from 0 to 1 .

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = } \\ { f ( x ) = \sqrt { \cos ( e ^ { x ^ { 5 } \sin ( x ) } ) } } \\ { \frac { 5 x ^ { 4 } e ^ { x ^ { 5 } \cdot \sin ( x ) } \cdot - \sin ( e ^ { x ^ { 5 } \cdot \sin ( x ) } ) \cdot - \sin ( x ) - x ^ { 5 } e ^ { x ^ { 5 } \cdot \sin ( x ) } \cdot \sin ( e ^ { x ^ { 5 } \cdot \sin ( x ) } ) \cos ( x ) } { 2 \sqrt { \cos ( e ^ { x ^ { 5 } \sin ( x ) } ) } } } \end{array} \right. \)