KS Connected Rate of Change The chain rule can be used to solve problem involving rates of change....
3
KS Connected Rate of Change The chain rule can be used to solve problem involving rates of change. Example 1 The length of the side of a square is increasing at a constant rate of 1.5 cm/s. At the moment when the length is of the side is 10 cm, find the rate of the increase of the area. Given 1.5, require dl dr dt dt 2 2 dA A l l dl The chain rule: 2 1.5 2 10 1.5 dA dA dl l dt dl dt 2 1 30cm s
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Transcript of KS Connected Rate of Change The chain rule can be used to solve problem involving rates of change....
KS
Connected Rate of Change
The chain rule can be used to solve problem involving rates of change.
Example 1The length of the side of a square is increasing at a constant rate of 1.5 cm/s. At the moment when the length is of the side is 10 cm, find the rate of the increase of the area.
Given 1.5, requiredl dr
dt dt 2 2
dAA l l
dl
The chain rule: 2 1.5 2 10 1.5dA dA dl
ldt dl dt
2 130cm s
KS
Connected Rate of Change
Example 2The length of the edge of a cube is increasing at a constant rate of 4.2 mm s-1. At the moment when the length of the edge is 50 mm, find the rate of increase of the volume.
Given 4.2, requiredl dv
dt dt 3 23
dVV l l
dl
The chain rule: 2 23 4.2 3 50 4.2dV dV dl
ldt dl dt
3 131500mm s
3 131.5cm s
KS
Connected Rate of Change
Example 3The area of a circle is decreasing at a rate of 1.4 cm2 s-1. Find the rate of change of the circumference when the radius is 5cm.
Given 1.4, requiredA dC
dt dt 2 2
dAA r r
dr
The chain rule: 1 141.4
2 5 100
dr dr dA
dt dA dt
10.28cms
142
100
dC dC dr
dt dr dt
