Mathematics · JEE | APPLICATION OF DERIVATIVES

Given below two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The function \( f(x) = x^3 - 3x^2 + 3x - 100 \) is strictly increasing on \( \mathbb{R} \). Reason (R): If \( f'(x) > 0 \) for all \( x \in \mathbb{R} \), then \( f(x) \) is strictly increasing on \( \mathbb{R} \). In the light of the above statements, choose the correct answer from the options given below:

1. A
   Both (A) and (R) are true and (R) is the correct explanation of (A).
2. B
   Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
3. C
   (A) is true but (R) is false.
4. D
   (A) is false but (R) is true.