# Mathematics - Calculus

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For the function:

y(x) = x^2 - 4.1x + 1.7

find the instantaneous rate of change of the function at x = 2. Compare the instantaneous rate of change to the average rate of change on the interval [1.9, 2.0].

(Please see the attached file)

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

y = x^2 - 4.1x + 1.7

(a) dy/dx = 2x - 4.1

dy/dx at x = 2 is 2(2) - 4.1 = -0.1

(b) Average rate of change = [2^2 - 4.1 * 2 + 1.7 - (1.9^2 - 4.1 * 1.9 + 1.7)] / (2 - 1.9) = -0.2

The magnitude of the instantaneous rate of change < The magnitude of the average rate of change.

Â© BrainMass Inc. brainmass.com September 29, 2022, 9:43 pm ad1c9bdddf>https://brainmass.com/math/basic-calculus/instantaneous-rate-change-function-219136