Answered: Use f(x)=x^3-2x^2+x and g(x)=3f(x+1)-2…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 50E

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Use f(x)=x^3-2x^2+x and g(x)=3f(x+1)-2 to do the following

d) Determine the average rate of change between and . Show your work.(1,(1))g(2,(2))ge)

Answer the following questions:

i) What kind of function is g(x)? Explain your answer.

ii) What is the domain and range of g(x)? Explain your answer.

iii) Use algebra to determine whether g(x) is an even function, an odd function or neither? Explain your answer.

iv) What are the x- and y-intercepts of g(x)? Explain your answer. Round to the nearest hundredths if appropriate.v) Determine the end behavior of g(x). Explain your reasoning.

vi) Find the local maximum and local minimum values of g(x). Round to the nearest hundredths if appropriate.

vii) Determine the intervals of g(x) is increasing and decreasing.

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