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Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ₀^ 2 f(x) d x=11 Question: What is f^ (0) equal to?

Options

  1. A18
  2. B16
  3. C15
  4. D14

Correct answer

D. 14

Step-by-step solution

P+Q+R=6 P+2+3=6 P=1 f(x)=e^x+2 e^ 2 x +3 e^ 3 x f^ (x)=e^x+2 2 e^ 2 x +3 3 e^ 3 x f(0)=1+4+9=14

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