a. Explanation The given function is f ( x ) = 1 3 x 3 − x 2 + x − 6 . Find the critical points to find the increasing and decreasing intervals. To find the critical points, set the first derivative to 0. f ( x ) = 1 3 x 3 − x 2 + x − 6 f ′ ( x ) = x 2 − 2 x + 1 = ( x − 1 ) 2 Set ( x − 1 ) 2 = 0 and solve for x . ( x − 1 ) 2 = 0 x − 1 = 0 x = 1 Therefore, the critical point divides the real line into two parts such as ( − ∞ , 1 ) ∪ ( 1 , ∞ ) b. To determine The relative extrema of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 . c. To determine The intervals on which the graph of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 concave upward and concave downward. d. To determine The inflection point of the function f ( x ) = 1 3 x 3 − x 2 + x − 6 .

10th Edition

ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

See similar textbooks

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Videos

Question

Chapter 4, Problem 1RE

To determine

The intervals on which the function f(x)=13x3−x2+x−6 is increasing and decreasing.

To determine

The relative extrema of the function f(x)=13x3−x2+x−6.

To determine

The intervals on which the graph of the function f(x)=13x3−x2+x−6 concave upward and concave downward.

To determine

The inflection point of the function f(x)=13x3−x2+x−6.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 10CRQ

Chapter 4, Problem 2RE

Students have asked these similar questions

(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.

(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =

(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0

Chapter 4 Solutions

APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN

Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E

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.

The intervals on which the function f ( x ) = 1 3 x 3 − x 2 + x − 6 is increasing and decreasing.

Solution Summary: The author explains the intervals on which the function f(x) is increasing and decreasing. The critical points divide the real line into two parts.

Concept explainers

Videos

The intervals on which the function f(x)=13x3−x2+x−6 is increasing and decreasing.

The relative extrema of the function f(x)=13x3−x2+x−6.

The intervals on which the graph of the function f(x)=13x3−x2+x−6 concave upward and concave downward.

The inflection point of the function f(x)=13x3−x2+x−6.

Want to see the full answer?

Chapter 4 Solutions