Consider the following statements : Statement-I : The function f(x)= x^3+128 x has a minimum value 48 at x=4. Statement-II : As x increases through 4, f'(x) changes sign from positive to negative. Which one of the following is correct in respect of the above statements?

NDA 2025 Mathematics question

Mathematics Application of Derivatives NDA 2025

Consider the following statements : Statement-I : The function has a minimum value 48 at . Statement-II : As increases through 4, changes sign from positive to negative. Which one of the following is correct in respect of the above statements?

(A)Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
(B)Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
(C)Statement-I is correct but Statement-II is not correctCorrect
(D)Statement-I is not correct but Statement-II is correct

Answer: (C)

Solution

, so , which is zero at . For slightly less than 4, and for slightly greater than 4,

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Question ID VK-030231