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The graph of the first derivative $f^{\prime}$ of a function $f$ is shown.(a) On what intervals is $f$ increasing? Explain.(b) At what values of $x$ does $f$ have a local maximum or minimum? Explain.(c) On what intervals is $f$ concave upward or concave downward? Explain.(d) What are the $x$ -coordinates of the inflection points of $f ?$ Why?

A. $f$ increases over the intervals $(2,4)$ and $(6,9)$B. $f$ has a local minimum at $x=2$ and $x=6$ and a local maximum at $x=4$C. Graph is concave up when $x \in(1,3) \cup(5,7) \cup(8,9)$Graph is concave down when $x \in(0,1) \cup(3,5) \cup(7,8)$D. So $f(x)$ has points of inflection at $x=1,3,5,7,8$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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The graph of the first der…

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(a) Find the intervals on …

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OK so clearly for Pat A. The increasing interval should be from 2 to 4 in the union with six to infinity, and the decreasing intervals should be from 0 to 2. You mean wave 4 to 6 end of From this result, we know there is a local minimum had X equals two and X equal to six and there is a local maximum at X equals 24 for Passy the functions concave upward on the interval. 123 union with 5 to 7 union weighs eight to infinity and this concave downward on the rest sits from 0 to 1 union with 3 to 5 in the union with 7 to 8. That means we have inflection points at X equals toe 1357 and eight because at those points the activity, if trending either from up

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