URGENT CALCULUS QUESTION: unbounded behavior and continuity

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1. Suppose C(x) is a function representing the cost (in dollars) of producing x units of energy, and R(x) is a function representing the revenue (in dollars) of selling x units of energy. Suppose further that both functions are continuous for all x > = 0. A. Is there necessarily some x value, let's call it C, that will maximize prot over all x > = 0'? Explain your answer. B. Suppose we know we can't produce more than 1,000 units of energy. Is there necessarily some xvalue, call it C, that will maximize prot over the interval [0,1000]? Explain your answer. C. Again, assume that we can't produce more than 1,000 units of energy. Is there necessarily some x value, let's call it C, for which the prot is exactly 0? Explain your