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Mathematics
Problem
A twice-differentiable function
m
m
m
satisfies
∣
m
′
′
(
t
)
∣
≤
0.6
|m''(t)|\le 0.6
∣
m
′′
(
t
)
∣
≤
0.6
for all
t
t
t
in the interval
[
3
,
3.1
]
[3,3.1]
[
3
,
3.1
]
. An estimate of
m
′
(
3
)
m'(3)
m
′
(
3
)
is formed with the quotient
m
(
3.1
)
−
m
(
3
)
0.1
\dfrac{m(3.1)-m(3)}{0.1}
0.1
m
(
3.1
)
−
m
(
3
)
. Determine a numerical upper bound for the absolute error of this estimate.
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