Question: Let ( h ) be a continuous function over the interval ([-8,8]) with derivative given by ( h )' consisting of two line segments and
Let \( h \) be a continuous function over the interval \([-8,8]\) with derivative given by \( h \)' consisting of two line segments and two semicircles, as shown in the graph. Part A: For what intervals is the graph of \( h \) increasing? Decreasing? Justify your answer. (10 points) Part B: For what value(s) of \( x \) does \( h \) have relative extrema? Justify your answer. (5 points) Part C: For what intervals is the graph of \( h \) concave up? Concave down? Justify your answer. (10 points) Part D: For what value(s) of \( x \) does \( h \) have a point of inflection? Justify your answer. (5 points)
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