Let f ( x ) = { 3 x + ∣ a 2 − 4∣ , − x 2 + 2 x + 7 , x < 1 x ≥ 1 . Then the set of values of a for which f ( x ) has a maximum value at x = 1 is:

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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

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Let $f (x) = {3 x + ∣ a^{2} - 4∣, - x^{2} + 2 x + 7, x < 1 x \geq 1$ . Then the set of values of $a$ for which $f (x)$ has a maximum value at $x = 1$ is:

Options:

Answer:

Solution:

Since $- x^{2} + 2 x + 7$ takes maximum value 8 at $x = 1$ , so $f (x)$ take maximum value at $x = 1$ , if $lim_{x \to 1} f (x) \leq f (1)$

$\Rightarrow a^{2} - 4 \leq 5 \Rightarrow a \in [- 3, 3]$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

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