3 (2) Let f(x) = r5/3 – 3x/3. Find and classify all critical points, all intervals of increase/decrease, and concavity information for f. Use this information to sketch the graph of f.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.3: Partial Fractions
Problem 2E
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(2) Let f(x) =
5/3 – 3x/3. Find and classify all critical points, all intervals of increase/decrease,
and concavity information for f. Use this information to sketch the graph of f.
(3) Let f(x) =1-x². Let P be the partition of [-1, 1] consisting of n subintervals of equal length.
Compute Lp(f), Up(f).
(4) Let f(x) = 1 – x2. Prove f is integrable on [-1,1] using either the definition or the e-
characterisation of integrability from the "Week 14" activities. (Hint: make use of #3.)
Transcribed Image Text:3 (2) Let f(x) = 5/3 – 3x/3. Find and classify all critical points, all intervals of increase/decrease, and concavity information for f. Use this information to sketch the graph of f. (3) Let f(x) =1-x². Let P be the partition of [-1, 1] consisting of n subintervals of equal length. Compute Lp(f), Up(f). (4) Let f(x) = 1 – x2. Prove f is integrable on [-1,1] using either the definition or the e- characterisation of integrability from the "Week 14" activities. (Hint: make use of #3.)
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