f(x) = x^5-5x Find the critical numbers of f. Determine the intervals on which f is increasing or decreasing. f is increasing on f is decreasing on Use the First Derivative Test to determine whether each critical point is a relative maximum, minimum, or neither. Relative maxima occur at x = relative minima occur at x =

f(x) = x^5-5x Find the critical numbers of f. Determine the intervals on which f is increasing or decreasing. f is increasing on f is decreasing on Use the First Derivative Test to determine whether each critical point is a relative maximum, minimum, or neither. Relative maxima occur at x = relative minima occur at x =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 15T

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(a) Find the critical numbers of f , if any (b) find the open intervals on which the function is increasing or decreasing, (c) apply the First Derivative Test to indentify all relative extrema and (d) use a graphing ulitulty to confirm your results. f(x)=x2-3x-4/x-2
Find all the critical points and horizontal and vertical asymptotes of the function f(x)=(x^2+5)/(x-2). Use the First and/or Second Derivative Test to determine whether each critical point is a local maximum, a local minimum, or neither. You may use either test, or both, but you must show your use of the test(s). You do not need to identify any global extrema.
f(x) = x3 - 2x2 - 15x + 36 = (3 - x)(12 - x - x2) Find the (a) intervals on which f is decreasing and increasing as well as the critical values of f(x), if any; (b) coordinates of local maximum and minimum values (if any); (c) intervals on which f is concave up and concave down as well as the points of inflection, if any; Sketch the graph of and show all details on the graph.
Find the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x) = 2x3 − 24x + 8 Step 1 Recall that a critical point is any interior point x in the domain of f where f '(x) = 0 or f '(x) is not defined. To find the critical points of g(x), first find the first derivative g'(x). Since g(x) = 2x3 − 24x + 8, then g'(x) = x2 − 24.
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Use the first derivative to find all critical points and use the second derivative to find all inflection points. Use a graph to identify each critical point as a local maximum, a local minimum, or neither. f(x) = x4 − 2x2 f(x) = x^5 − 5x^4 + 35
(A) find the critical numbers of f, if any (B) find the open intervals on which the function is increasing or decreasing (C) apply the First Derivative Test to identify all relative extrema
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Find the critical points and the intervals on which the function f(x)=9x5−3x3+6f(x)=9x5−3x3+6 is increasing or decreasing. Use the First Derivative Test for each critical point to determine whether it is a local minimum or maximum (or neither). (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list. Enter NULL if there are no critical points.) Open interval(s) where sign of the derivative implies the function is increasing: help (intervals) Open interval(s) where sign of the derivative implies the function is decreasing: help (intervals) Critical point(s) with local minimum: c=c= help (numbers) Critical point(s) with local maximum: c=c= Critical point(s) without a local min or max: c=c=
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