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Suppose lim x→[infinity] f(x) = 60 and f '(x) is positive for all x. Assuming lim x→[infinity] f '(x) exists, find its value. Hint: You might want to sketch a possible graph of f(x) . lim x→[infinity] f '(x) =

Answer :

Given that lim x->∞ f(x) = 60 and f'(x) is positive for all x, we can determine the value of lim x->∞ f'(x).

Given that limx→∞f(x) = 60 and f'(x) is positive for all x, we can determine the value of limx→∞f'(x).

Since f'(x) is positive for all x, it means that the graph of f(x) is continuously increasing as x approaches infinity. This indicates that the slope of the graph of f(x) is positive at every point, resulting in a positive derivative.

Therefore, limx→∞f'(x) will be greater than zero because the derivative of f(x) is positive for all x.

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