question_answer

Direction: For the following questions, choose the correct answers from the codes [a], [b], [c] and [d] defined as follows.

Let \[f(x)\] be a function such that \[f'(x)\,=\,\prod\limits_{n\,=\,1}^{10}{{{(x-n)}^{n}}}\].

Statement I The sum of all values of \[x\]at which \[f(x)\] attains minima is 15.

Statement II\[f(x)\] has inflectional points at \[x=2,\,4,\,6,\,\,8,\,\,10\]

A)  Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I.

B)  Statement I is true. Statement II is also true and Statement n is not the correct explanation of Statement I.

C)  Statement I is true. Statement II is false.

D)  Statement I is false. Statement II is true.

Correct Answer: A

Solution :

 \[f(x)\] has inflectional points at \[x=2,\,4,\,6,\,8,\,10\]. Maximum at \[x=3,\,7\] and minimum at \[x=1,\,\,5,\,\,9\]. \[\therefore \] Sum of minimum values of \[x=1+5+9=15\]