Determine the Number of Distinct Real Solutions

Very Hard Data Sufficiency Determining Sufficiency

Consider a function defined by the equation f(x) = 2x^3 - 6x^2 + 4x - 8. We want to determine the number of distinct real solutions to the equation f(x) = 0.

Statement (1): The function has a local maximum at x = 1.

Statement (2): The derivative of the function, f'(x), has two distinct real roots.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Hint

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