Question

Let f be the function defined as follows.

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

(a) Find the differential of f.
dy=(16x-2)dx
(b) Use 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 =

(c) Find 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 =

Answer 1

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