In Exercises 4756, (a) plot the points, (b) find the distancebetween the points, and (c) find the midpoint of the linesegment joining the points.4, 10, 4, 5
Step 1 of 3
Minimum and maximum values Let c be a number in the domain of f. f(c) is a local max if f(c) ≥ f(x) when x is near c. f(c) is a local min if f(c) ≤ f(x) when x is near c Fermat’s Theorem: If f has a local max or min at c, and if f’(c) exists, then f’(c)’=0 Be careful: The converse of this theorem is not always true. Consider f(x) = x^3 f’(x) = 3x^2 f’(0) = 3*0^2 =0 However there is no min/ max at x=0 the tangent line is horizontal there. Consider f(x) = [x] F has a minimum at x = 0; however f’(0) does not exist. Consider f(x) = √x f has a minimum at x = 0 f’(x) = 1/√x f’(0) = 1/2 0 d oes not exist The tangent line is vertical there Def. a critical number of a function f is a number c in the domain of f such that either f’(c) = 0 or f
Textbook: College Algebra
Author: Ron Larson
This full solution covers the following key subjects: . This expansive textbook survival guide covers 62 chapters, and 5693 solutions. The full step-by-step solution to problem: 49 from chapter: P.6 was answered by , our top Math solution expert on 03/09/18, 08:01PM. The answer to “In Exercises 4756, (a) plot the points, (b) find the distancebetween the points, and (c) find the midpoint of the linesegment joining the points.4, 10, 4, 5” is broken down into a number of easy to follow steps, and 27 words. This textbook survival guide was created for the textbook: College Algebra , edition: 8. College Algebra was written by and is associated to the ISBN: 9781439048696. Since the solution to 49 from P.6 chapter was answered, more than 231 students have viewed the full step-by-step answer.