(a)
(b)
(c)
(d)
Figure N4–20where f (a) + f ′(a)(x − a) is the linear or tangent-line approximation for f (x), and
f ′(a)(x − a) is the approximate change in f as we move along the curve from a to
x. See Figure N4–20.
In general, the closer x is to a, the better the approximation is to f (x).
Example 30 __
Find tangent-line approximations for each of the following functions at the
values indicated:
sin x at a = 0
cos x at a =
2 x^3 − 3x at a = 1
SOLUTIONS: