JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 24th February Evening Shift
Question
Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) 0 for all x R. If \left| {\matrix{
{f(x)} & {f'(x)} \cr
{f'(x)} & {f''(x)} \cr
} } \right| = 0, for all xR, then the value of f(1) lies in the interval :
Choose an option
Show full solutionCorrect option: D
Correct answer
D(6, 9)
Step-by-step explanation
\left| {\matrix{
{f(x)} & {f'(x)} \cr
{f'(x)} & {f''(x)} \cr
} } \right| = 0
Dividing by , we get
Integrating both side,
(constant)
At, ,
at x = 0,
So it lie between (6, 9).
Dividing by , we get
Integrating both side,
(constant)
At, ,
at x = 0,
So it lie between (6, 9).
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