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Limits Continuity and Differentiability question

2019 · Shift 1 · Q30

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2019 · Shift 1 · Q30

Limits Continuity and Differentiability question

2019 · Shift 1 · Q30

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1

Let f : R

\to

R be given by

f(x) = \left\{ {\begin{matrix} {{x^5} + 5{x^4} + 10{x^3} + 10{x^2} + 3x + 1,} & {x \lt 0;} \\ {{x^2} - x + 1,} & {0 \le x \lt 1;} \\ {{2 \over 3}{x^3} - 4{x^2} + 7x - {8 \over 3},} & {1 \le x \lt 3;} \\ {(x - 2){{\log }_e}(x - 2) - x + {{10} \over 3},} & {x \ge 3;} \\ \end{matrix} } \right\}

Then which of the following options is/are correct?

A
f is increasing on ( $- \infty$ , 0)
B
f' is not differentiable at x = 1
C
f is onto
D
f' has a local maximum at x = 1

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