Key Concepts Sect 6.2
Relative Maximum: greatest value of the points in a certain region.
Relative Minimum: Least value of the points in a certain region.
Multiple Zeros: a linear factor of a polynomial that is repeated.
Multiplicity: equal to the number of multiple zeros.
Guided Practice Sect 6.2
Ex 1: Write (x ­ 1)(x + 3)(x + 4) as a polynomial in standard form.
Ex 2: Write in factored form.
b.) 6x3 ­ 15x2 ­ 36x
a.) 3x3 ­ 18x2 + 24x
Guided Practice Sect 6.2
Ex 3: An airline has carry­on luggage regulations. The sum of the length, width, and depth may not exceed 50 in.
a.) assume that the sum of the length, width, and depth is 50 in. and the length is 10 in greater then the depth. Graph the function relating the volume V to depth x. Find the x­intercepts. What do they represent?
b.) Describe a realistic domain for V(x).
c.) What is the maximum possible volume of the box? What are the dimensions of the box?
Guided Practice Sect 6.2
Ex 4: Find the zeros of y = (x + 1)(x ­ 1)(x + 3) then graph the function.
Ex 5: Write a polynomial function in standard form with zeros at 2, ­3, and 0.
Ex 6: Find any multiple zeros of f(x) = x5 ­ 6x4+9x3 and state the mulitplicity.
Homework
Sect 6.2: p.317 3­12 every 3rd, 14, 15­54 every 3rd, 58