Math 1271, Summer 2010, Worksheet 35.11. Let f(x) = x5/3− 20x2/3. Find the critical points of f(x). Use the first derivative testto determine which critical values give a local maximum and which give a local minimumfor f(x). Second, test values using the second derivative test.2. The function f (x) is continuous and has the following properties:(a) f0(−2) = 0, f0(3) = 0, f0(10) = DNE, f00(0) = 0, f00(3) = 0, and f00(10) = DNE.(b) f0(x) > 0 when −2 < x < 3 or 3 < x < 10. Also, f0(x) < 0 when x < −2 or x > 10.(c) f00(x) > 0 when x < 0, 3 < x < 10, or x > 10. Also, f00(x) < 0 when 0 < x < 3.This function has 3 critical points. What are they? Using the second derivative test,determine which critical points give f a local maximum, which give f a local minimum, andwhich give f neither.Do the above problem over again by using the first derivative test to see if the 3 criticalpoints result in maxima, minima or neither.1Math 1271, Summer 2010, Worksheet 35.21. Let f(x) = (2x+1)3/2+(22− x)3/2for −1/2 < x < 22. Find all the values of x such thatf(x) has a local minimum value and the values of x such that f(x) has a local maximumvalue. Include endpoints.2. A storage room is to be constructed with a volume of 9,000 ft3. It is to have a squarebase. Material for the bottom costs $5 per ft2, material for the top costs $3 per ft2, andmaterial for the sides costs $12 per ft2. Find the length of one side of the base and the heightin order that the cost of material to construct the room is a
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