Describe in words the general shape of the graph if a and b

Question

Question: Let y = Ae^x + 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.