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GATE 2016 CE (CE2) – Question 40

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 2 marks · Multiple choice

The quadratic approximation of $f(x)=x^3-3x^2-5$ at $x=0$ is ______.

  1. $3x^2-6x-5$
  2. $-3x^2-5$
  3. $-3x^2+6x-5$
  4. $3x^2-5$

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Correct answer: (B) $-3x^2-5$

Explanation

Taylor’s quadratic polynomial is f(0)+f-prime(0)x+f-double-prime(0)x²/2. Here f(0)=−5,f-prime(0)=0 and f-double-prime(0)=−6. Thus the approximation is **−3x²−5, B**. The x³ term contributes only at cubic order.