Explanation Given: The function is f ( x ) = x 3 − 6 x 2 + 12 x − 11 . Approach: Need to identify all relevant features of the graph of this function, i.e., its domain, critical points, regions over which it is increasing or decreasing, points of inflection, regions over which it is concave up or concave down, intercepts, and asymptotes. After that graph the function, showing all these features. Calculation: Consider the function. f ( x ) = x 3 − 6 x 2 + 12 x − 11 ……. (1) Differentiate Equation (1) with respect to x . f ′ ( x ) = 3 x 2 − 12 x + 12 = 3 ( x 2 − 4 x + 4 ) = 3 ( x − 2 ) 2 …… (2) Substitute 0 for f ′ ( x ) in Equation (2) 0 = 3 ( x − 2 ) 2 x = 2 , 2 Substitute 2 for x in Equation (1). f ( 2 ) = ( 2 ) 3 − 6 ( 2 ) 2 + 12 ( 2 ) − 11 = − 3 Therefore, the critical points for the function is ( 2 , − 3 ) . Since, the differential function is positive. Thus, the function do not decrease over any interval and the function is increasing over the interval ( − ∞ , 2 ) and ( 2 , ∞ )

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

See similar textbooks

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

Videos

Question

Chapter 5.4, Problem 6E

To determine

To Graph:

The function by considering the domain, critical points, symmetry, regions where the function is increasing or decreasing, inflection point, regions where the function is concave upward or concave downward, intercepts where possible and asymptotes where applicable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.4, Problem 5E

Chapter 5.4, Problem 7E

Students have asked these similar questions

Find dydx for y=tan(5x)/7e3x.dy/dx =

Differentiate f(w)=8w^5f'(w)=

Differentiate the following function. You do not need to simplify the derivative. f(x)=ln(4x2+x−3) f'(x)=

Chapter 5 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 5.1 - YOUR TURN Find where the function is increasing...Ch. 5.1 - YOUR TURN 2 Find the intervals in which...Ch. 5.1 - Prob. 3YT Ch. 5.1 - YOUR TURN Find where f is increasing and...Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Find the open intervals where the functions...Ch. 5.1 - Prob. 6E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To Graph: The function by considering the domain, critical points, symmetry, regions where the function is increasing or decreasing, inflection point, regions where the function is concave upward or concave downward, intercepts where possible and asymptotes where applicable.

Solution Summary: The author analyzes the graph of the function by considering its domain, critical points, symmetry, inflection point, regions where it is increasing or decreasing, intercepts, and asymptotes.