If f′(x)=2x+a≥0∀x∈[1,2]⇒a≥−2x∀x∈[1,2]
amin=R=−2 If
amax=S=−4
∣R−S∣=2
Alternate :
If f(x) is increasing for all x∈[1,2] then
−2a≤1⇒a≥−2⇒R=−2
If f(x) is decreasing for x∈[1,2], then
−2a≥2⇒a≤−4⇒S=−4
∣R−S∣=2
JEE Main 2021 — Mathematics Calculus
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
Held on 31 Aug 2021 · Verified 6 Jul 2026.
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