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4. (12 points) The function f(x) = A cosh (Cr) + B sinh (Ca) features three constants A, B and C. Answer the following questions to determine the values of A, B and C (using the assumption that C > 0) so that f(x) satisfies the conditions "(x) = 36 . S(x) (1) f (0) = -2, S'(0) = 12 ( 2 ) (A) (7 points) Use condition (1) to determine the value of the constant C > 0. (B) (5 points) Use conditions (2) to determine the values of A and B Note: Condition (1) is an example of a differential equation, and condition (2) is often called "initial conditions." Solving dif- ferential equations subject to initial conditions is a main topic of study in various other mathematics and applied mathematics courses