Quiz 3 Math G140 Name: Please Show All Work, if needed! Place answers in ANSWER box, if provided. 1. (3 points) Use implicit differentiation to find the slope of the tangent line to the curve at the given point. x2+2xy-yz+x=20, (4,8) 2. (3 points) A box with an open top is to be constructed from a square piece of cardboard with dimensions 8 cm x 8 cm. This box is constructed by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. 2)Page 2 of 2 3. (4 points) Sketch the graph of this function using the following guidelines: J (x) = x5 - 3x2 a) Intercept(s), if any: - intercept(s) = y - intercept = b) Increasing and decreasing intervals (in interval notation): Increasing interval = Decreasing interval = c) Local Maximum and Minimum Point(s): Local Maximum Point = Local Minimum Point = d) Concave up and concave down intervals (in interval notation): Concave up interval = Concave down interval = e) Inflection Point(s), if any: Inflection Point = Inflection Point = f) Graph: QUAWNHOHNWAGO -6 - 5 -4 -3 -2 -1 1 2 3 456