MATH 101 HOMEWORK 1
Due on Wednesday Sept. 10
1. (5 marks) Find all values of k such that the line y = 3x − 4 is tangent to the graph of
y = kx3 .
2. (5 marks) A ladder 12 ft long rests against a vertical wall. If the bottom of the ladder
slides away from the wall at a rate of 1 ft/s. how fast is the top of the ladder sliding down
the wall when the bottom of the ladder is 4 ft from the wall?
3. (5 marks) A box with an open top is to be constructed from a rectangular piece of
cardboard of size 3 ft × 2 ft 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.
4. (5 marks) Sketch the graph of the function y = x2x−4 . Include the following information:
local minima and maxima, intervals of increase and decrease, intervals of concavity and
inflection points, asymptotes, limits at infinity.
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