   Chapter 2.9, Problem 19E

Chapter
Section
Textbook Problem

# 19-22 Compute Δ y and dy for the given values of x and d x = Δ x . Then sketch a diagram like Figure 5 showing the line segments with lengths dx, dy, and Δ y . y = x 2 − 4 x ,   x = 3 ,   Δ x = 0.5

To determine

To compute:

y and dy for the given values of x and dx=x and sketch a diagram showing the line segment dx, dy and y

Explanation

1) Formula:

i. y=fx+x-f(x)

ii. dy=f'xdx

2) Given:

y=fx=x2-4x

3) Calculation:

By using formula,

y=fx+x-f(x)

Since, x=3 and x=0.5

y=f3+0.5-f(3)

y=f3.5-f(3)

Since, y=fx=x2-4x

y=3.52-43.5-32+4(3)

y=12.25-14-9+12=1.25

Therefore,  y=1

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