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Limits Continuity and Differentiability question

2022 · 26 Jul · Shift 1 · Q32

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 26 Jul · Shift 1 · Q32

Limits Continuity and Differentiability question

2022 · 26 Jul · Shift 1 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f(x) = \left\{ {\begin{matrix} {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \\ { - 2x + {{\log }_2}({b^2} - 4),} & {x \gt 1} \\ \end{matrix} } \right.

. Then the set of all values of b, for which f(x) has maximum value at x = 1, is :

A
( $-$ 6, $-$ 2)
B
(2, 6)
C
$[ - 6, - 2) \cup (2,6]$
D
$\left[ {-\sqrt 6 , - 2} \right) \cup \left( {2,\sqrt 6 } \right]$

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