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MATH 16A WORKSHEET 7-
(1) Find all relative maxima and minima of the function f(x) = (1/3)x3 - (5/2)x2 + 4x + 1 and indicate whether each point is a minimum or maximum.
(2) Is the function f(x) = -(1/2)x4 concave up or down at x = 0?
(3) Find the quadratic function f(x) = ax2 + bx + c that goes through (-1, 6) and has a local minimum at (2, 1).
(4) Find the minimum of Q = x2 + y2 if x + y = 6. Is there an absolute maximum?
(5) Find two positive numbers x and y whose sum is 13 and whose product is as large as possible.
Find the Equation of the line which passes through the two given points and Solve the system using the graphing method.
A farmer has 80m length of fencing. He wants to use it to form three sides of a rectangular enclosure against an existing fence which provides the fourth side. Find the maximum area that he can enclose and give its dimensions.
Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31
What is the point of the vertex? How does this number relate to your answers in parts e and f?
Find a vector function that represents the curve of intersection of x2 + y2 = 4 and z =x. Find the normal plane of the curve above at the point (0,2,0).
Determine the number of fence posts, placed 1 meter apart, needed to make a 100 meter fence.
Suppose the proportion of women who favor stricter gun control legislation is pw and the proportion of men who favor stricter gun control legislation is pm. The survey found a 90% confidence interval for pw-pm IS (-.08,.22). Give an interpretation..
Suppose the output of the steam plant is described by a vector that lists the amounts of heat, sulfur dioxide, and particulate matter. Express this output as a linear combination of two vectors, assuming that the plant burns x1 tons of A and x2 to..
In a report on high school graduation, it was stated that 85% of high school student graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that all graduate?
Compare the mean of the sample means with the population mean.
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
In a box there are 7 red spheres and 12 blue spheres. 2 spheres are taken without return. If the third sphere is red, what is the probability that 2 first spheres are blue ?
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