JEE Main 2021 — Application Of Derivatives Question with Solution
From: JEE Main 2021 (Online) 22th July Evening Shift
Question
Let f : R R be defined as
f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.. Then f is increasing function in the interval
f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.. Then f is increasing function in the interval
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Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
f'(x)\left\{ {\matrix{
{ - 4{x^2} + 4x + 3} & {x > 0} \cr
{3{e^x}(1 + x)} & {x \le 0} \cr
} } \right.
For x > 0,
f(x) is increasing in
For x 0, f'(x) = 3ex(1 + x)
f'(x) > 0 x (1, 0)
f(x) is increasing in (1, 0)
So, in complete domain, f(x) is increasing in
For x > 0,
f(x) is increasing in
For x 0, f'(x) = 3ex(1 + x)
f'(x) > 0 x (1, 0)
f(x) is increasing in (1, 0)
So, in complete domain, f(x) is increasing in
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