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Question: Let y = Aex + Be-x for any constants A, B.
(a) Sketch the graph of the function for
(i) A = 1, B = 1
(ii) A = 1, B = 1
(iii) A = 1, B = 1
(iv) A = 1, B = 1
(v) A = 1, B = 1
(vi) A = 1, B = 1
(b) Describe in words the general shape of the graph if A and B have the same sign. What effect does the sign of A have on the graph?
(c) Describe in words the general shape of the graph if A and B have different signs. What effect does the sign of A have on the graph?
(d) For what values of A and B does the function have a local maximum? A local minimum? Justify your answer using derivatives.
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