In the following exercises, the maximum of the right-hand side of the remainder estimate on | R 1 | ≤ max | f " ( z ) | 2 R 2 on [ a - R , a + R ] occurs at a or a ± R. Estimate the maximum value of R such that max | f " ( z ) | 2 R 2 ≤ 0.1 on [ a - R, a + R ] by plotting this maximum as a function of R . 136. [T] e x approximated by 1 + x . a = 0
In the following exercises, the maximum of the right-hand side of the remainder estimate on | R 1 | ≤ max | f " ( z ) | 2 R 2 on [ a - R , a + R ] occurs at a or a ± R. Estimate the maximum value of R such that max | f " ( z ) | 2 R 2 ≤ 0.1 on [ a - R, a + R ] by plotting this maximum as a function of R . 136. [T] e x approximated by 1 + x . a = 0
In the following exercises, the maximum of the right-hand side of the remainder estimate on
|
R
1
|
≤
max
|
f
"
(
z
)
|
2
R
2
on [a-R, a+R] occurs at a or a ± R. Estimate the maximum value of R such that
max
|
f
"
(
z
)
|
2
R
2
≤
0.1
on [a - R, a + R] by plotting this maximum as a function of R.
Find the smallest a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0,a].
In Exercises 11–22, find: (a) the intervals on which ƒ is in- creasing, (b) the intervals on which ƒ is decreasing, (c) the open intervals on which f is concave up, (d) the open inter- vals on which f is concave down, and (e) the x-coordinates of all inflection points.
11. f(x) = x² – 5x +6
Find the smallest integer a such that the Intermediate Value Theorem guarantees that f(x) has a zero on the interval [0,a].
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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