Consider the function  f(x)=x^3−3x^2+6.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the function 

f(x)=x^3−3x^2+6.

a) This function has two critical points (x,y). Identify both of them. Just type x and y values, do not use parentheses. Order them so that x is in ascending order. For example, if there are two points (-2,5) and (3,-2), then type (-2,5) first and (3,-2) last.

b.) b) Determine the intervals on which f is increasing. For −∞ type  -100 and for +∞ type 100.

f is increasing on =

c.) Complete the sentence: The function f attains its relative maximum value at x=Answer and its relative minimum value at x=

d.) Determine the interval on which f is concave down. For −∞ type  -100 and for +∞ type 100.

f is concave down on =

e.) Find the absolute maximum and minimum values of f on the interval [1,5]. If an absolute maximum or minimum does not exist, enter NONE.

Absolute minimum value of f= 

Absolute maximum value of f=

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