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GATE 2020 EE – Question 36

Engineering Mathematics · Calculus: Maxima and minima · 2 marks · Multiple choice

For real numbers, $x$ and $y$, with $y=3x^2+3x+1$, the maximum and minimum value of $y$ for $x\in[-2,0]$ are respectively,

  1. 7 and 1/4.
  2. 7 and 1.
  3. $-2$ and $-1/2$.
  4. 1 and 1/4.

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Show answer and explanation

Correct answer: (A) 7 and 1/4.

Explanation

$y'=6x+3=0$ at $x=-\frac12$, where $y=\frac34-\frac32+1=\frac14$ (a minimum). At the ends, $y(-2)=12-6+1=7$ and $y(0)=1$. So the maximum is 7 and the minimum is $\frac14$.