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Answer:
The instantaneous rate of change of with respect to
at the value
is 18.
Step-by-step explanation:
a) Geometrically speaking, the average rate of change of with respect to
over the interval by definition of secant line:
(1)
Where:
,
- Lower and upper bounds of the interval.
,
- Function exaluated at lower and upper bounds of the interval.
If we know that ,
and
, then the average rate of change of
with respect to
over the interval is:
The average rate of change of with respect to
over the interval
is 27.
b) The instantaneous rate of change can be determined by the following definition:
(2)
Where:
- Change rate.
,
- Function evaluated at
and
.
If we know that and
, then the instantaneous rate of change of
with respect to
is:
The instantaneous rate of change of with respect to
at the value
is 18.