Locating critical points a. Find the critical points of the following functions on the domain or on the given interval. b. Use a graphing unity In determine whether each critical point corresponds to a local minimum. local maximum. or neither. ? ? ? f(? ? ) = si? cos x? on [0, 2?]
Step 1 of 3
STEP_BY_STEP SOLUTION Step-1 Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 0 1 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). 4 2 Example ; Find all critical points of f(x) = x 8x . Because f (x) is a polynomial function, its domain is all real numbers. 1 3 f (x) = 4x 16x f (x) = 0 =4x 16x 2 4x ( x - 4) = 0 2 4x(x+2)(x-2) = 0 , since a - b = (a+b)(a-b) X = 0 , x = -2 and x=2. 4 2 At x= -2 , then f(-2) = ( 2) 8( 2) = 16 - 32 = -16. At x= 0 , then f(0) = (0) 8(0) = 0 - 0 = 0. 4 2 At x= 2 , then f(2) = (2) 8(2) = 16 - 32 = -16. Hence, the critical points of f(x) are (2,16), (0,0), and (2,16). Step-2 a). The given equation is ; f(x) = sin(x) cos(x) , here f(x) is trigonometric function and it is continuous for all...
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 28E from chapter: 4.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: critical, points, local, corresponds, domain. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Locating critical points a. Find the critical points of the following functions on the domain or on the given interval. b. Use a graphing unity In determine whether each critical point corresponds to a local minimum. local maximum. or neither. ? ? ? f(? ? ) = si? cos x? on [0, 2?]” is broken down into a number of easy to follow steps, and 53 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 28E from 4.1 chapter was answered, more than 318 students have viewed the full step-by-step answer.