Consider the following : 1. f(2)=f(1)-f(0) 2. f"(2)-2f'(1)=12 Which of the above is/are correct? [NDA I 2016]

Correct Answer is : Both 1 and 2

Correct Answer is : Both 1 and 2

Test Index

UPSC NDA I 2016 Mathematics Solved Paper

For the next three (3) items that follow :

Let

f:\mathbb{R}\rightarrow\mathbb{R}

be function such that

f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)

for

x\in\mathbb{R}

[NDA I 2016]

Question : 64 of 120

Marks: +1, -0

Consider the following :

f(2)=f(1)-f(0)

f"(2)-2f'(1)=12

Solution:

f(1)-f(0)=4-6

=-2

f(2)=8-20+4+6=-2

Hence

f(2)=f(1)-f(0)

∴Statement (1) is correct

f''(2)-2f'(1)=2-2(-5)

f''(2)-2f'(1)=12

∴Statement (2) is correct

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