A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold \( 15 \mathrm{yd}^{3} \) of debris. Find the dimensions of the dumpster that will minimize its surface area.

b) \( f(x)=2 x^{3}+x^{2}-5 x+2 \)

What is the general form of an antiderivative for \( f(x) = 3x^{2} \)?

\( y ^ { 3 } \sin ( 2 x ) d x - 3 y ^ { 2 } \cos ^ { 2 } x d y = 0 \)

a) \( f(x)=\tan (3 x) \) 8) Mediante derivación implicita, ob tenga la derivada con respecto a \( \frac{x}{x^{2} y^{2}+1} \) \( \begin{array}{ll}\text { a) } 3 x^{5} y^{3}+2 x^{4}=x^{3} & \text { b) } x^{3}-y^{4}+3=\operatorname{sen}\left(x^{3} y\right)\end{array} \)

Ti lafunaín es \( f(x)=x^{3}+4 x^{2}-3 x \) Derivar Resduel la derwada. Dartevalor antes ucuno despoes.