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Let f(x) = 3^(x^2-2x) + 4, x ∈ R. Then which of the following statements are true ? P : x = 0 is a point of local minima of f Q : x = √2 is a point of inflection of f R : f' is increasing for x > √2

1. Only P and Q
2. Only P and R
3. Only Q and R
4. All, P and R

Correct answer: All, P and R

Solution

The function f(x) has a local minimum at x = 0 because the first derivative changes from negative to positive, indicating a minimum point. At x = √2, the second derivative changes sign, confirming it as a point of inflection. Additionally, the first derivative f' is increasing for x > √2, which supports the correctness of statements P and R.

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