JEE Main 2021 — Application Of Derivatives Question with Solution
From: JEE Main 2021 (Online) 31st August Morning Shift
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 |R S| is ___________.
the value of |R S| is ___________.
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Show full solutionCorrect answer: 2
Correct answer
2
Step-by-step explanation
f(x) = x2 + ax + 1
f'(x) = 2x + a
when f(x) is increasing on [1, 2]
2x + a 0 x[1, 2]
a 2x x[1, 2]
R = 4
when f(x) is decreasing on [1, 2]
2x + a 0 x[1, 2]
a 2 x[1, 2]
S = 2
|R S| = | 4 + 2 | = 2
f'(x) = 2x + a
when f(x) is increasing on [1, 2]
2x + a 0 x[1, 2]
a 2x x[1, 2]
R = 4
when f(x) is decreasing on [1, 2]
2x + a 0 x[1, 2]
a 2 x[1, 2]
S = 2
|R S| = | 4 + 2 | = 2
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