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GATE 2017 CE (CE2) – Question 36

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

At which point does the tangent to $y=x\ln x$ make 45° with the x-axis?

  1. (1,0)
  2. (0,1)
  3. (1,1)
  4. $(\sqrt2,\sqrt2)$

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Correct answer: (A) (1,0)

Explanation

The required slope is $\tan45^\circ=1$. Differentiate: $dy/dx=\ln x+1$. Setting this equal to 1 gives $x=1$, then $y=1\ln1=0$. The point is (1,0), option A.