Answer to Question #64135 in Calculus for Janette A. Merenillo

Question

I-ANALYTIC GEOMETRY/RECTILINEAR MOTION
1.Find the tangent line as directed to the curve Y = X4 + 2X3 – 2X2 -3X + 3 perpendicular to the line: X – 3Y = 2.
2.Find the tangent of the line as directed to the curve Y = X4 + 4X3 – 8X2 + 3X + 70 with slope 3.
3.Find the equation of the line tangent to the curve Y = 3X2 – 4X and parallel to the line X – 2Y + 6 = 0.
4.Find the equation of each normal line to the curve Y= X3 – 4X that is parallel to the line X + 8Y -8 = 0.
5.A particle moves along a straight line according to the law: S = 132 + 10t – 6t2 + 3t3. Find: a.) velocity and acceleration at any time t? b.) Velocity at t = 2 and c.) Acceleration at t= 3.
II-MAXIMA AND MINIMA
1.A box with a square base is to have an open top. The area of the material in the box is to be 100 in square. What should the dimensions be in order to make the volume as large as possible?