1. 3.6 Polynomial and Rational Inequalities 3.7 Variation
College Algebra
3.6 Polynomial and Rational Inequalities
3.7 Variation

2. 3.6 Polynomial Inequalities Obj: solve polynomial and rational inequalities with the critical value method
Critical Value Method
Zeros (solutions) of polynomials are called the critical points.
Critical Points of a polynomial divide positive values from negative values.

3. Example Solve x2 – 2x – 15 < 0
Factor and solve for x. These are the critical points.
Choose a value in each interval.
Let x =
Plug each value into the factored form ( + or - ).
Compare relations.
Write solution in interval notation.

4. Rational Inequalities
Steps:
Set = to 0 and simplify.
Find the zeros of the numerator and denominator to find the critical points.
Test the intervals.
Compare the relations.
Write the solution.

5. Example
Solve

6. 3.7 Variation Obj: to set up and solve problems using variation
Direct Variation
Inverse Variation
Joint Variation
Combined Variation

7. Direct Variation Varies directly or is directly proportional to
Meaning as one unit increases, the other increases or as one decreases, the other decreases also
y = kx k is the constant of
proportionality
Examples:

8. Example
The distance d that a ball rolls down an inclined plane is directly proportional to the square of time t. If the ball rolls 5 feet in 1 second, how far will it roll in 4 seconds?
Set up the equation using initial info.
Solve for k.
Set up new equation with k value
and new info.
Solve.

9. Inverse Variation
Varies inversely or is inversely proportional to Meaning as one unit increases, the other decreases and vice versa. y = Examples:

10. Example
The speed v of a gear varies inversely as the number of teeth t. If a gear that has 48 teeth makes 20 revolutions per minute, how many revolutions per minute will a gear that has 30 teeth make?

11. Joint Variation more than one variable
z = kxy
The cost of a concrete patio varies jointly as the area of the patio and the depth of the patio. It costs $500 for a patio with an area of 80 square feet and a depth of 4 inches. Find the cost of a patio with an area of 144 square feet and a depth of 6 inches.

12. Combined Variation more than one type of variation
The volume of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If the volume of the gas is 220 cm3 when T = 40˚C and P = 20 kg/cm2, what is the volume when T = 35˚C and P = 10 kg/cm2?

13. Assignment 3.6 page 420 1 – 13 eoo, 29 – 45 eoo