91Ó°ÊÓ

Sketch the graph of the polynomial function described, or explain why no such function can exist. The expression complex zero will be used to mean a nonreal complex number. Cubic function with two distinct negative zeros, one positive zero, and a positive \(y\) -intercept.

Sketch the graph of the polynomial function described, or explain why no such function can exist. The expression complex zero will be used to mean a nonreal complex number. Cubic function with a negative double zero and a positive zero, and a negative leading coefficient.

The number of kilograms of "payload" an airplane can carry equals the number of kilograms the wings can lift minus the mass of the airplane, minus the mass of the crew and their equipment. Use these facts to write an equation of the payload as a function of the airplane's length. \(\cdot\) The plane's mass is directly proportional to the cube of the plane's length. \(\cdot\) The plane's lift is directly proportional to the square of the plane's length. a. Assume that a plane of a particular design and length \(L=20 \mathrm{m}\) can lift \(2000 \mathrm{kg}\) and has a mass of \(800 \mathrm{kg}\). Write an equation for the lift and an equation for the mass as functions of \(L\) b. Assume that the crew and their equipment have a mass of \(400 \mathrm{kg}\). Write the particular equation for \(P(L)\), the payload the plane can carry in kilograms. c. Make a table of values of \(P(L)\) for each \(10 \mathrm{m}\) from 0 to \(50 \mathrm{m}\) d. Function \(P\) is cubic and thus has three zeros. Find these three zeros, and explain what each represents in the real world.

Sketch the graph of the polynomial function described, or explain why no such function can exist. The expression complex zero will be used to mean a nonreal complex number. Quartic function with no real zeros

Sketch the graph of the polynomial function described, or explain why no such function can exist. The expression complex zero will be used to mean a nonreal complex number. Quartic function with two distinct positive zeros, two distinct negative zeros, and a negative \(y\) -intercept

Enter into your journal what you have learned so far about higher-degree polynomial functions. Include such things as shapes of the graphs and constant differences and their relationship to the degree of the polynomial.

Sketch the graph of the polynomial function described, or explain why no such function can exist. The expression complex zero will be used to mean a nonreal complex number. Quartic function with two distinct real zeros and two complex zeros

Find the derivative function, \(f^{\prime}(x) .\) Use the fact that the derivative is zero at an extreme point to find the \(x\) -coordinates of all extreme points. Confirm your answer graphically. Save the graphs of Problems 17 and 18 for Problems 23 and 24 $$f(x)=x^{3}-12 x^{2}+36 x+17$$

What is the difference in meaning between an indeterminate form and an infinite form?

Find a particular equation of the cubic function, with zeros as described, if the leading coefficient equals \(1 .\) Then find the zeros and confirm that your answers satisfy the given properties. Sum: \(4 ;\) sum of the pairwise products: -11 product: -30.