Concavity and Curve Sketching Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(2) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(3) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(4) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(5) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(6) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(7) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(8) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(9) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(10) Identify the inflection points and local maxima and minima of the function Identify the intervals on which the function is concave up and concave down. Sketch the graph showing these specific features.

(11) Sketch a smooth curve with for for for and for

(12) Sketch the graph of the following function Find all vertical and horizontal asymptotes of the graph of each function. Determine intervals of increasing and decreasing, determine concavity, and locate all critical points and points of inflection. Show all special features such as cusps or vertical tangents.

(13) Sketch the graph of the following function Find all vertical and horizontal asymptotes of the graph of each function. Determine intervals of increasing and decreasing, determine concavity, and locate all critical points and points of inflection. Show all special features such as cusps or vertical tangents.

(14) Find constants and that guarantee that the graph of the function defined by will have a vertical asymptote at and a horizontal asymptote at Sketch the graph of the function.

(15) Find all vertical tangents and cusps for the function Justify your work. Sketch the graph of the function.

(16) Find all vertical tangents and cusps for the function . Justify your work. Sketch the graph of the function.

(17) Explain why the function has a vertical asymptote but no vertical tangent. Sketch the graph of the function.

(18) Sketch the graph of the curve for [ ). Show all special features such as vertical asymptotes, horizontal asymptotes, cusps, vertical tangents, and intercepts. Sketch the graph of the function.

Cite this as:
Concavity And Curve Sketching Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/concavity-and-curve-sketching-homework.html