H-H 2.4 The Second Derivative

Intro, Part I

Intro, Part II

Example 1

Example 2

Example 3

Poll: the temperature outside on a given day is given by \( f(t){}^\circ C, \) where \( t \) is in hours since midnight. From 6 AM until noon, the first derivative was negative and the second was positive. Which of the following is correct? You may choose more than one.

(a) The temperature was below freezing but getting warmer.
(b) The temperature was below freezing and getting colder.
(c) We do not no whether the temperature was above or below freezing.
(d) The temperature was higher at noon than at 6 AM.
(e) The temperature was lower at noon than at 6 AM.
(f) The temperature was rising but at a slower rate as the morning progressed.
(g) The temperature was rising but at a faster rate as the morning progressed.
(h) The temperature was falling and at a faster rate as the morning progressed.
(i) The temperature was falling but at a slower rate as the morning progressed.

Example 4

Self-Checks

By Lisa Oberbroeckling

I am a mathematician and faculty member in the Mathematics and Statistics Department at Loyola University Maryland in Baltimore. I have my B.S. in mathematics from the University of Iowa and my M.S. and Ph.D in mathematics from the University of Oregon. My dissertation is entitled "Generalized Inverses in Certain Banach Algebras" advised by Dr. Bruce Barnes. My research is currently in applying my functional analysis background to numerical analysis: finite-element methods for solving systems of differential equations in collaboration with Dr. Christos Xenophontos (University of Cyprus). I have designed and taught a course in MATLAB and I know have a published textbook Programming Mathematics Using MATLAB.

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