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Application of Derivatives question

2012 · Shift 2 · Q30

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2012 · Shift 2 · Q30

Application of Derivatives question

2012 · Shift 2 · Q30

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −1

If

f\left( x \right) = \int_0^x {{e^{{t^2}}}} \left( {t - 2} \right)\left( {t - 3} \right)dt

for all

x \in \left( {0,\infty } \right),

then

A
$f$ has a local maximum at $x=2$
B
$f$ is decreasing on $(2, 3)$
C
there exists some $c \in \left( {0,\infty } \right),$ such that $f'(c)=0$
D
$f$ has a local minimum at $x=3$

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