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The document in the OP A man has $\displaystyle 75\pi \text{ cm}^2$ sheet of metal and wishes to make an open cylindrical container with it. Find the dimension of the tin for which the volume will be maximum.
Find the stationary points of the function $\displaystyle y = x^2(3+2x-3x^3)$ and investigate their nature.
Find the gradient to the tangent to the curve $\displaystyle x^2+2xy-2y^2+x =2$ at the point $\displaystyle (-4,1)$
Find the equation of the tangent and normal to the curve $\displaystyle y = 3x^2-9x+4$ at the point $\displaystyle x=2$
Find the equation of the normal line to the curve $\displaystyle y=4x^3-5x^2+2$ at the point $\displaystyle (-1,-7)$