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Question

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 |RS| is

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Solution

Given: f(x)=x2+ax+1
f(x)=2x+a
For increasing function 2x+a|x=10
a2
For decreasing function 2x+a|x=20
a4
R=2,S=4
|RS|=2

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