×
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4 - Problem 14re
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4 - Problem 14re

×

# Curve sketching Use the guidelines of this | Ch 4 - 14RE ISBN: 9780321570567 2

## Solution for problem 14RE Chapter 4

Calculus: Early Transcendentals | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Calculus: Early Transcendentals | 1st Edition

4 5 1 395 Reviews
19
0
Problem 14RE

Curve sketching? Use the guidelines of this chapter to make a complete graph of the following functions on their domains or on the given interval. Use a graphing utility to check your work. f(x) = x +3

Step-by-Step Solution:

Solution Step 1 In this problem we need to make a complete graph of f(x) = 2x in its domain or in the x +3 given interval. Since the interval is not mentioned, we take the domain. Here in the given function equate denominator to 0, we get x =± 3i, therefore the domain is {x; x = / ± 3i} . In order to sketch the complete graph, we need to find the critical points, inflection points, local maximum and local minimum if possible. First let us see the definitions: Critical point: An interior point cof the domain of a function f at which f (c) = 0or f(c)fails to exist is called a critical point of f Inflection Point: An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. A necessary condition for x to be an inflection point is f (x) = 0 Local maximum: Let f be function defined on an interval [a,b]and let pbe a point in the open interval (a,b). Then the function f has local maximum at pif f(p) f(x) for all xin the neighborhood of the point p. Local minimum: Let f be function defined on an interval [a,b]and let pbe a point in the open interval (a,b). Then the function f has local minimum at pif f(p) f(x)for all x in the neighborhood of the point p.

Step 2 of 6

Step 3 of 6

##### ISBN: 9780321570567

Unlock Textbook Solution