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Let f(x)=1/x, Find the number b such that the average rate of change of f on interval (2,b) is -(1/10).

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Final answer:

To find the number b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to solve a quadratic equation derived from the average rate of change formula.

Step-by-step explanation:

To find the number b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to calculate the average rate of change of f and then set it equal to -(1/10). The average rate of change of a function on an interval is given by the formula: average rate of change = (f(b) - f(a))/(b - a). In this case, we have f(x) = 1/x and the interval is (2, b). So, we need to set up the equation: (1/b) - (1/2))/(b - 2) = -(1/10).

To solve this equation, we can multiply both sides by 10(b - 2) to eliminate the denominators. This will give us a quadratic equation that we can solve for b.

User Daniel Dawes
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