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Let f be the function defined as follows.

y=f(x)=(8x^2)-2x+3

AFind the differential of f.

dy=(16x-2)dx

BUse your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two decimal places.)

dy =

CFind the actual change in y if x changes from 2 to 1.97 and compare your result with that obtained in part (b). (Round your answer to two decimal places.)

Δy =

Verified Answer :

nobillionaireNobley

y = f(x) = 8x^2 - 2x + 3
a.) dy/dx = 16x - 2

b.) dy = (16x - 2)dx
dy = (16(2) - 2)(2 - 1.97) = 0.03(32 - 2) = 0.03 * 30 = 0.9
dy = 0.9

c.) (8(2)^2 - 2(2) + 3) - (8(1.97)^2 - 2(1.97) + 3) = 31 - 30.1072 = 0.8928
Δy = 0.8928

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