   Chapter 3.1, Problem 26E

Chapter
Section
Textbook Problem

# Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Use the graphs and transformations of Sections 1.2 and 1.3.) f ( x ) = 1 − x 3

To determine

To sketch:

The graph of a function f by hand and then find the absolute and local maximum and minimum values of f.

Explanation

1) Concept:

Sketch graph of f, and then use definitions of absolute and local maximum and minimum values of f.

2) Definitions:

i) Let c be a number in the domain D of a function f. Then f(c) is the absolute maximum value of f on D if fc f(x) for all x in D and absolute minimum value of f on D if fcf(x) for all x in D.

ii) The number f(c) is a local maximum value of f  if fcf(x) when x is near c and local minimum value of f if fc fx  when x is near c.

Fermat’s theorem in terms of critical numbers:

If f has a local maximum or minimum at c, then c is a critical number of f.

3) Given:

fx=1-x3

4) Calculation:

Sketch the graph of f(x):

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