a. Suppose the function s(t) gives the position of a particle along a number line, measured in meters, at time t seconds. If both s' (t) < 0 and s"(t) < 0 on the interval (4, 7) then the particle's speed is increasing on the time interval from 4 to 7 seconds. b. If f"(3) = 0 then f must have an inflection point at (3, f(3)) c. The function g(x) = ln(x² + 2x + 1) is never concave up.

a. Suppose the function s(t) gives the position of a particle along a number line, measured in meters, at time t seconds. If both s' (t) < 0 and s"(t) < 0 on the interval (4, 7) then the particle's speed is increasing on the time interval from 4 to 7 seconds. b. If f"(3) = 0 then f must have an inflection point at (3, f(3)) c. The function g(x) = ln(x² + 2x + 1) is never concave up.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Determine whether the following statements are true or false. You must clearly state TRUE or FALSE, and provide a justification/explanation/counterexample to demonstrate why the statement is true or false.

a. Suppose the function s(t) gives the position of a particle along a number line, measured in meters, at time
t seconds. If both s' (t) < 0 and s" (t) < 0 on the interval (4, 7) then the particle's speed is increasing on
the time interval from 4 to 7 seconds.
b. If f"(3) = 0 then f must have an inflection point at (3, f(3))
C.
The function g(x) = In(x? + 2x + 1) is never concave up.

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