Page 41 - How To Solve Word Problems In Calculus

m = ∆f(x)
sec ∆x
= f(x + h) − f(x)
h
f(x + h)

∆f(x) = f(x + h) − f(x)
= f (x)
f(x)
m tan

h = ∆x
x x + h

EXAMPLE 1
(a) Find the average rate of change of the area of a square with
respect to its side x as x changes from 4 to 7.
(b) Find the rates of change of the area of a square with respect
to its side x when x = 4, 5, 6, and 7.

Solution
2
(a) A(x) = x . The average rate of change of A(x) with respect
A(x)
to x is .
x

A(x) = x 2
A(4) = 16 A(7) = 49

A(x) = A(7) − A(4) = 33

x = 7 − 4 = 3
A(x) 33
= = 11
x 3
Alternatively,
2
A(x) = x , x = 4, h = 3

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