If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then
the value of |R $-$ S| is ___________.
Answer (integer)
2
Solution
f(x) = x<sup>2</sup> + ax + 1<br><br>f'(x) = 2x + a<br><br>when f(x) is increasing on [1, 2]<br><br>2x + a $\ge$ 0 $\forall$ x$\in$[1, 2]<br><br>a $\ge$ $-$2x $\forall$ x$\in$[1, 2]<br><br>R = $-$4<br><br>when f(x) is decreasing on [1, 2]<br><br>2x + a $\le$ 0 $\forall$ x$\in$[1, 2]<br><br>a $\le$ $-$2 $\forall$ x$\in$[1, 2]<br><br>S = $-$2<br><br>|R $-$ S| = | $-$4 + 2 | = 2
About this question
Subject: Mathematics · Chapter: Application of Derivatives · Topic: Increasing and Decreasing Functions
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