Explanation Given information: The statement “If f has a local minimum at x = p then f ' ( p ) = 0. ” The statement “If f has a local minimum at x = p then f ' ( p ) = 0. ” is not always true, there is another possibility if f has a local minimum at x = p , then f ' ( p ) can also be UNDEFINED. For any function f, a point p in the domain of f where f ‘ ( p ) = 0 or f ‘ ( p ) is undefined is called a critical point of the function. In addition, the point ( p , f ( p ) ) on the graph of f is also called a critical point. A critical value of f is the value, f ( p ) , at a critical point, p Geometrically, at the critical point where f ' ( p ) = 0 , the line tangent to the graph of f at p is horizontal

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 4, Problem 10SYU

To determine

To indicate:

Whether the statement is true or false.

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Chapter 4, Problem 9SYU

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

K Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. x-7 p(x) = X-7 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = OB. f is discontinuous at the single value x= OC. f is discontinuous at the two values x = OD. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - ∞. The limit for the smaller value is The limit for the larger value is The limit for the smaller value is The limit for the larger value does not exist and is not c∞ or -

Chapter 4 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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To indicate: Whether the statement is true or false.

Solution Summary: The author indicates whether the statement is true or false. If f has a local minimum at x=p, it can also be UNDEFINED.