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A differentiable function f(x) satisfies f(0) = 2, f'(0) = 3 and f''(x) = f(x). If the graph of y = f(x) meets the x-axis at x = (1/a) ln(1/5), find the value of a.

1. 1
2. 2
3. -1
4. 5

Correct answer: 2

Solution

Solving f'' = f with the given initial data gives f(x) = (5/2)e^x - (1/2)e^(-x); setting it to zero gives e^(2x) = 1/5, i.e. x = (1/2)ln(1/5), so a = 2.

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