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Application of Derivatives question

2019 · Shift 2 · Q20

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2019 · Shift 2 · Q20

Application of Derivatives question

2019 · Shift 2 · Q20

JEE AdvancedMathematicsApplication of DerivativesMultiple correct+4 / −1

Let f : R

\to

R be given by

f(x) = (x - 1)(x - 2)(x - 5)

. Define

F(x) = \int\limits_0^x {f(t)dt}

, x > 0 Then which of the following options is/are correct?

A
F(x) $e$ 0 for all x $\in$ (0, 5)
B
F has a local maximum at x = 2
C
F has two local maxima and one local minimum in (0, $\infty$ )
D
F has a local minimum at x = 1

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