Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.
A)
B)
C)
D)
E)

Question

​Compare dy and Δy for  at ​x​ = -1 with Δ​x​ = dx = 0.01.Give your answers to four decimal places. ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

To find dy, we need to take the derivative of the function and evaluate it at x=-1. Thus, 
dy = f'(-1)dx = (-4 + 4 + 6 - 8)/4 (-0.01) = -0.005

To find Δy, we need to plug in x=-1 and x=-1+dx=-0.99 into the function and take the difference. Thus, 
Δy = f(-0.99) - f(-1) = 0.99^4 - (-1)^3 + 2(-0.99)^2 - (-1) - 5 = 0.0415

Out of the choices given, only option B has a Δy value that is closest to -0.005.

​Compare Dy and ΔY for at ​X​ = -1

Compare Dy and ΔY for at X = -1