In Problems 53-74, summarize the pertinent information obtainedby applying the graphing strategy and sketch the graph of y = f(x). 65. f(x) = 2x6 - 3x³

Answered: f(x) = 2x² - 3x²

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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Question

In Problems 53-74, summarize the pertinent information obtained
by applying the graphing strategy and sketch the graph of y = f(x).

Expert Solution

Step 1: Introduction:

Given: The function $f left parenthesis x right parenthesis equals 2 x to the power of 6 minus 3 x to the power of 5$ .

To sketch the graph of the given function.

Concepts Used :

The points at which $f left parenthesis x right parenthesis equals 0$ are known as the zeroes of the function. For zeroes with odd multiplicity the graph intersects the $x$ -axis at that value. For zeroes with even multiplicity the graph touches the $x$ -axis at that point.

If $f apostrophe left parenthesis x right parenthesis greater than 0$ at each point of an interval $I$ , then the function $f left parenthesis x right parenthesis$ is said to be increasing on that interval. If $f apostrophe left parenthesis x right parenthesis less than 0$ at each point of an interval $I$ , then the function $f left parenthesis x right parenthesis$ is said to be decreasing on that interval. If $f apostrophe left parenthesis x right parenthesis equals 0$ , then $x$ is known as the critical point of the function.

If $f apostrophe apostrophe left parenthesis x right parenthesis greater than 0$ at each point of an interval $I$ , then the function $f left parenthesis x right parenthesis$ is concave up in that interval. If $f apostrophe apostrophe left parenthesis x right parenthesis less than 0$ at each point of an interval $I$ , then $f left parenthesis x right parenthesis$ is concave down in that interval. If $f apostrophe apostrophe left parenthesis x right parenthesis equals 0$ , then $x$ is known as the inflection point of the function.

Differentiation formula:

$fraction numerator d over denominator d x end fraction left parenthesis x to the power of n right parenthesis equals n x to the power of n minus 1 end exponent$