Let f be the function defined as follows.

Question

Let f be the function defined as follows.

y = f(x) = 5x² − 9x + 5

(a)    Find the differential of f.

dy = 

 

(b)    Use your result from part (a) to find the approximate change in y if x changes from 7 to 6.88. (Round your answer to four decimal places, if necessary.)

dy = 

(c)    Find the actual change in y if x changes from 7 to 6.88. (Round your answer to four decimal places, if necessary.)

Δy = 

(d)    Compare your result in part (c) with that obtained in part (b) by calculating the absolute value of their difference.

|dy − Δy| = 

Answer 1

(a) dy = y'dx = (10x - 9)dx

(b) dy = y'(7)dx = (70 - 9)(6.88 - 7) = - 7.32

(c) Δy = f(6.88) - f(7) = 179.752 - 187 = - 7.248

(d)Idy - ΔyI = I - 7.32 + 7.248I = 0.072