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Miscellaneous·2016·Easy

Let f : R → R be a function such that f(x) = x³ + x²f′(1) + xf″(2) + f‴(3) for x ∈ R. Consider the following : 1. f′(2) = f(1) − f(0) 2. f″(2) − 2f′(1) = 12 Which of the above is/are correct?

Let f : R → R be a function such that
f(x) = x³ + x²f′(1) + xf″(2) + f‴(3)
for x ∈ R. Consider the following :

1. f′(2) = f(1) − f(0)

2. f″(2) − 2f′(1) = 12

Which of the above is/are correct?

Options

  1. a.
    1 only
  2. b.

    2 only

    Correct answer
  3. c.

    Both 1 and 2

  4. d.

    Neither 1 nor 2

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