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Limits Continuity and Differentiability question

2018 · Shift 1 · Q22

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2018 · Shift 1 · Q22

Limits Continuity and Differentiability question

2018 · Shift 1 · Q22

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −1

For every twice differentiable function

f:R \to [ - 2,2]

with

{(f(0))^2} + {(f'(0))^2} = 85

, which of the following statement(s) is(are) TRUE?

A
There exist r, s $\in$ R, where r < s, such that f is one-one on the open interval (r, s)
B
There exists x0 $\in$ ( $-$ 4, 0) such that |f'(x0)| $\le$ 1
C
$\mathop {\lim }\limits_{x \to \infty } f(x) = 1$
D
There exists $\alpha \in$ ( $-$ 4, 4) such that f( $\alpha$ ) + f"( $\alpha$ ) = 0 and f'( $\alpha$ ) $e$ 0

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