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GATE 2021 ME (ME1) – Question 44

Engineering Mathematics · Calculus: Limit, continuity, differentiability, mean value theorems and indeterminate forms · 2 marks · Multiple choice

Let $f(x)=x^2-2x+2$ be a continuous function defined on $x\in[1,3]$. The point $x$ at which the tangent of $f(x)$ becomes parallel to the straight line joining $f(1)$ and $f(3)$ is

  1. 0
  2. 1
  3. 2
  4. 3

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Show answer and explanation

Correct answer: (C) 2

Explanation

The secant slope is $[f(3)-f(1)]/(3-1)=(5-1)/2=2$. A parallel tangent must satisfy f′(x)=2.

Since f′=2 x−2, solve 2 x−2=2 to get **x=2 (C)**.