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Let a function f(x) be such that f''(x) = f'(x) + e x and f(0) = 0, f'(0) = 1 then ln ⁡ f 2 2 4   i s   ?

Options

  1. A1/2
  2. B1
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

Let f'(x) = V dV dx + V - 1 = e x ⇒ Ve - x = ∫ e x e - x dx ⇒ Ve - x = x + C 1 f ' 0 = 1 ⇒ C 1 = 1 ⇒ f ' x = xe x + e x ⇒ f x = xe x + C 2 f 0 = 0 ⇒ C 2 = 0 ⇒ f x = xe x ⇒ f 2 = 2 e 2 ln f 2 2 4 = 4

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