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1. For the function f defined below, determine if f is increasing or decreasing at x=2 and determine the concavity at x=2. f(x) = x-1-x2
2. Suppose that the function f has the following characteristics:
f'(x) < 0 for 0 < x < 1f'(1) = 0f'(x) > 0 for 1 < x < 2
then
Question options:
f has a local minimum at x = 1.f has a local maximum at x = 1.f has neither a local maximum or a local minimum at x = 1.
there is not enough information to determine if x = 1 is a maximum or minimum.
3. Find the distance from the origin to the point on the line y=-2x+3 that is closest to the origin. Round your answer to two decimal places.
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Implement the following boolean function with a 4x1 multiplexer and external gates. Connect inputs A and B to the selection lines. The input requirements for the four data lines will be a function of variables C and D.
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Constraints, Decision variables, Objective functions
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the faculty senate at a large university wanted to know what proportion of the students thought a foreign language
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