Summarize how graphs can be used to find solutions to polynomial inequalities.

dictetzqh 2021-11-20 Answered
Summarize how graphs can be used to find solutions to polynomial inequalities.
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huckelig75
Answered 2021-11-21 Author has 11 answers

Step 1
1. If necessary, rewrite the inequality so that there is a zero on one side.
2. Graph the other side of the inequality.
3. Use your graphing calculator's TRACE function to the exact or approximate values of the x-intercepts.
4. Find the intervals that satisfy the inequality.
5. Write the final result as a solution interval.
Step 2
Example:
x34x2+x+53
1. We substract 3 from both sides of the inequality:
x34x2+x+20
2. We graph y=x34x2+x+2
image

Step 3
With the help of the graphing calculator we find the x-intercepts as x{0.562, 1, 3.562}, rounded to three decimal digits:
image Step 4
4. We note that the inequality is satisfied on the intervals (, 0.562] and 1, 3.562].
5. We write the result as a solution interval:
{xRx0.562 or 1x3.562}
or alternatively
x(, 0.562][1, 3.562]
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Provere
Answered 2021-11-22 Author has 18 answers

Step 1
Q2 has been attached here for reference:
Volume=2x330x2+100x
2x330x2+100x72
image

Step 2
The x-axis of the graph of a function is the number line over which the function is changing and therefore can be read to find the domain of x for different ranges of the value of f(x).
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