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Consider the function f(x) = { tan x / x, for x ≠ 0 { 1, for x = 0 Statement 1: x = 0 is a point of minimum of f. Statement 2: f'(0) = 0. Which of the following is correct?

1. Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.
2. Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.
3. Statement 1 is true, Statement 2 is false.
4. Statement 1 is false, Statement 2 is true.

Correct answer: Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.

Solution

At x = 0, the function f(x) achieves a minimum value of 1, making Statement 1 true. Statement 2 is also true because the derivative at that point is zero, indicating a critical point, but this does not directly confirm it as a minimum since further analysis is needed.

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