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
Open in App
Solution
Given: f(x)=x2+ax+1 f′(x)=2x+a
For increasing function 2x+a|x=1≥0 a≥−2
For decreasing function 2x+a|x=2≤0 a≤−4 R=−2,S=−4 |R−S|=2