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anonymous
 one year ago
Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3], (ii)[1,2], (iii)[1,1], (iv) [1,1.2], (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)).
begin (array)(cccccc) hline interval & [1,3] & [1,2] & [1,1] & [1,1.2] & [1,1.1] hline average rate of change & & & & & hline end (array)
Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.
anonymous
 one year ago
Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3], (ii)[1,2], (iii)[1,1], (iv) [1,1.2], (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)). begin (array)(cccccc) hline interval & [1,3] & [1,2] & [1,1] & [1,1.2] & [1,1.1] hline average rate of change & & & & & hline end (array) Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.

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