Let f be a differentiable function from the set of real numbers to itself, satisfying f'(x) > 2f(x) for every real number x, and given that f(0) = 1. Which of the following is true?

f(x) decreases over the interval (0, ∞)
f(x) is greater than e^(2x) for all x in (0, ∞)
f(x) is less than e^(2x) for all x in (0, ∞)
f(x) increases over the interval (0, ∞)

Correct answer: f(x) increases over the interval (0, ∞)

Solution

The function f(x) increases over the interval (0, ∞) because its derivative f'(x) is greater than 2f(x), indicating that the rate of change of f(x) is always positive, thus f(x) is an increasing function.

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