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Consider the function f(x) = {2x3 - x2 +3x if x < 2, -36 +31x - 2x2 if x greater than or equal to 2}
a. Explain why f(x) is continuous and differentiable.
b. Graph the function in the xy plane where both x and y are non-negative. Find the positive values of x over which the function is increasing and decreasing.
c. Calculate the derivative of the function and explain why the sign of the derivative makes sense given your answers to part (b).
d. In your graph in (b), what value(s) of x minimize(s) the function for the domain and range given in (b)? Is df/dx=0 for these values of x? Why or why not?
e. Explain why x=2 is a point of inflection for f(x).
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the diagonals of parallelogram abcd not shown are perpendicular. if one diagonal has a length of 10 and the other
hardware store sells house numerals. It has large quantities of the numerals 3, 5 and 8 but is out of all the others. How many different house numbers, with no more than three digits, can be made from these numerals?
Find marginal revenue function. What is the marginal revenue at q = 2. Solution : The total revenue (R) is given by R = q (25 + 6q - q2 ) = 25q + 6 q2 - q3.
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Thirty days later, after regular training supplemented by vitamin E, they are tested again. The new results are listed below. Use the Wilcoxon signed-rank test to find the critical value to test the claim that the vitamin E supplement
Determine the rate of change of the x-coordinate of the point Q at the moment when P is at (3,0) and the x-coordinate of P is increasing at a rate of 1 cm/sec.
What is the approximate probability that the blood test will be positive and so at least one person has the disease? Suppose that the blood test yields a positive result.
For the following right triangle, find the side length x. Round the answer to the nearest tenth.
Calculate aggregate expenditure in equilibrium where E=Y Calculate and interpret the individual and combined effects of changes to X0 and M0 such that X0 = 150 and M0 = 150 and all other variables remain unchanged. Also, calculate and interpret the v..
In this plane there sits a disk of radius 1 with conductivity . Normally this disk will distort the current flow as it is more conductive than the plane, however we will "cloak" this disk by placing an annulus 1 of less conductive material around the..
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