jee-main 2023 Q70

jee-main · India · session2_13apr_shift1 Curve Sketching Variation Table and Monotonicity from Sign of Derivative

Let $f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2(b^2 - 4), & x > 1 \end{cases}$. Then the set of all values of $b$, for which $f(x)$ has maximum value at $x = 1$, is
(1) $(-2, -1]$
(2) $[-2, -1) \cup (1, 2]$
(3) $(-2, 2)$
(4) $(-\infty, -2) \cup (2, \infty)$

Let $f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2(b^2 - 4), & x > 1 \end{cases}$. Then the set of all values of $b$, for which $f(x)$ has maximum value at $x = 1$, is\\
(1) $(-2, -1]$\\
(2) $[-2, -1) \cup (1, 2]$\\
(3) $(-2, 2)$\\
(4) $(-\infty, -2) \cup (2, \infty)$

Paper Questions

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