Question
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
UBMIT ANSWER
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
UBMIT ANSWER
Ask by Moran Robbins. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The net change in
from
to
is -432. The average rate of change is -36 units per unit
.
Solution
Let’s analyze the function
over the interval from
to
.
(a) Net Change
The net change in the function
between
and
is calculated as the difference between the value of the function at
and
.
-
Calculate
: -
Calculate
: -
Determine the Net Change:
Interpretation: The function
decreases by 432 units when
increases from -6 to 6.
(b) Average Rate of Change
The average rate of change of
over the interval from
to
is found by dividing the net change by the change in
.
-
Change in
: -
Average Rate of Change:
Interpretation: On average, the function
decreases by 36 units per unit increase in
over the interval from -6 to 6.
Summary:
- (a) The net change in
from to is . - (b) The average rate of change of
over this interval is units per unit .
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To determine the net change of the function
between
and
:
First, calculate
and
.
Next, find the net change:
Now for the average rate of change:
Thus, the answers are:
(a) Net change:
(b) Average rate of change:
(a) Net change:
(b) Average rate of change: