Calculate etA and use your answer to solve dx dt = Ax, x(0) = x0. a. A = _ 1 5 2 4 _ , x0 = _ 6 1 _ b. A = _ 0 1 1 0 _ , x0 = _ 1 3 _ c. A = _ 1 3 3 1 _ , x0 = _ 5 1 _ d. A = _ 1 1 1 3 _ , x0 = _ 2 1 _ e. A = 1 1 2 1 2 1 2 1 1 , x0 = 2 0 4 f. A = 1 2 2 1 0 1 0 2 1 , x0 = 3 1 4

Minimum and maximum values Let c be a number in the domain of f. f(c) is a local max if f(c) ≥ f(x) when x is near c. f(c) is a local min if f(c) ≤ f(x) when x is near c Fermat’s Theorem: If f has a local max or min at c, and if f’(c) exists, then f’(c)’=0 Be careful: The converse of this theorem is not always true. Consider f(x) = x^3 f’(x) = 3x^2 f’(0) = 3*0^2 =0 However...