Question

MAT 200 Maple Project Part 1 Due date: May 4, 2021

Submission Instructions: Submit ONE SINGLE PDF file as an attachment by responding to the

message with subject “MAPLE Project Part 1” on MyOpenMath. To produce a PDF file in Maple, go

to File -> Export as, and then select PDF.

Choose six integers 𝐴, 𝐵, 𝐶, 𝐷, 𝐸, 𝐹 between -10 and 10 but excluding 0. Use these

values in the problems below.

A=

B=

C=

D=

E=

F=

1. (10 points) Define the function 𝑓(𝑥) = 𝐴𝑥5 − 𝐵𝑥3 + 𝐷𝑥2 − 𝐸 and compute the

difference quotient 𝑓(𝑥+ℎ)−𝑓(𝑥)

ℎ . Do not forget to simplify.

2. (10 points) Graph the piecewise defined function 𝑓(𝑥) = { 𝐴𝑥𝐷 − 𝐵𝑥, 𝑖𝑓 0 < 𝑥 < 2

𝐶 + √|𝐹|𝑥, 𝑖𝑓 𝑥 ≥ 2

3. (10 points) Let 𝑓(𝑥) = 𝐵 − 𝐴𝑥 + 𝐹𝑥2. Graph the three functions 𝑓(𝑥), 𝐷𝑓(𝑥), 𝐷𝑓(𝑥) − 𝐹

on the same coordinate system.

4. (10 points) Graph the function 𝑓(𝑥) = 𝐴𝑥5 + 𝐵𝑥4 − 𝐶𝑥3 + 𝐷𝑥2 − 𝐸𝑥 + 𝐹. Find how

many x-intercepts and how many turning points the graph has.

5. (10 points) Graph the function 𝑓(𝑥) = 𝐴𝑥6 −𝐶𝑥4+ 𝐹𝑥 2+𝐵𝑥

𝐵𝑥5−𝐴𝑥3+𝐷𝑥2−𝐸 and its asymptotes. Find the

equations of all horizontal and vertical asymptotes.