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OpenStudy (anonymous):
Compute y/x for the interval [5,7], where y=5x-6. (Use decimal notation. Give your answer to three decimal places.) What is the instantaneous rate of change of y with respect to x at x=5? Rate= ?
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OpenStudy (aum):
y = 5x - 6 when x = 5, y = 5*5 - 6 = 25 - 6 = 19 when x = 7, y = 5*7 - 6 = 35 - 6 = 29 Average rate of change over the interval [5,7] = { f(7) - f(5) } / (7 - 5) = (29-19) / 2 = 10 / 2 = 5 What is the instantaneous rate of change of y with respect to x at x=5? The instantaneous rate of change is the slope of the line which is the same for all values of x. Instantaneous rate = 5.
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