1) graph a function given the following information:

• The instantaneous rate of change at x = 2 is zero.
• The instantaneous rate of change at x = 3 is negative.
• The average rate of change on the interval 0<=x<=4 is 0

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2)The air intake valve on a car tire completes a revolution of a circle with radius 10cm every 0.5 seconds. Assume that the valve starts at its lowest point at time zero.

a) Determine the equation of a sinusoidal function that models this situation.

b) Determine the valve's height after 2.3 seconds. Round your answer to two decimal places if necessary.