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Find: (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.$f(x)=e^{-x^{2} / 2}$

(a) $(-\infty, 0]$(b) $[0,+\infty)$(c) $(-\infty,-1),(1,+\infty)$(d) (-1,1)$(\mathbf{e})-1,1$

Calculus 1 / AB

Chapter 4

THE DERIVATIVE IN GRAPHING AND APPLICATIONS

Section 1

Analysis of Functions I: Increase, Decrease, and Concavity

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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so looking at this graph here, we see, um, that it's ah, increasing from infinity to zero. And then it's decreasing from zero to negative or affirmative affinities. Here it's increasing from infant zero to infinity, it's decreasing. It is, uh, Kong Cave from negative Infinity toe one. And then it is Kong cave down from negative one to positive one. And then, from then on it's Khan gave up from one to infinity, which tells us that the inflection points are negative one and positive one.

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