Calculus|NOPE|High School
The graph of g(x) is given. • g(x) has horizontal tangents at x = −5, x = −1.1, and x = 4. • g(x) has inflections points at x = −3.1, x = 1, and x = 4. • g(x) has zeros at x = −6.1, x = −3.1, and x = 2. (a) Complete and then use the chart showing the important points and characteristics of the graphs to sketch a graph of g'(x) on the same axes as g(x) above. (b) How many roots does g'(x) have and what are those values? Justify your answer. (c) On what intervals is g'(x) negative? Justify your answer. (d) On what interval(s) is g'(x) increasing? Justify your answer. (e) Where does g'(x) have local extremes and which type (min or max) occurs where? Justify your answer.
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