Mat 117 Problem Set 7 (Maximum and Minimum Values)

Mat 117 Problem set 7 (Maximum and minimum values)

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1. A parcel delivery service has contracted you to design an open box with square base length x cm and height y cm has a volume of 3600 cubic cm. Find the total surface area in terms of x and y. Also determine the dimension for minimum surface area (round answers correct to two decimal places if needed).

2. Use the rational zero theorem to find all rational zeroes, and use those zeroes to write f( x )= 2 x4 - x 3 - 9 x 2 + 4 x + 4 in factor form. 3. Determine a polynomial function of degree 3 with real coefficients whose zeroes are -2, 1 + i .

4. Given y=( x - 3)2 ( x + 4)( x + 2) . Find the following:

a) The power function

b) Maximum turning points

c) All zeroes

d) x -intercept(s)

e) y -intercept

f) Behavior near each x intercepts

g) Plot the function