Consider the function f(z) whose second derivative is f" (z) = 2z+5 sin(z). If f(0) = 4 and f'(0) = 6, find the actual function f(z). Student solution. First we begin by recalling the following antiderivatives: antiderivative of z = antiderivative of z = antiderivative of cos(z) =| antiderivative of sin(z) =. Using these rules, we can write for f'(z) the following f'(z) =+C for some constant c The value for the constant c is given as Thus the first derivative f'(z) equals f (2) =D Next we can compute f up to a constant co, namely: f(2) =+G. The value for the constant co is given as Thus the function f(z) equals f(r) =.

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