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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Consider the function $f : R \to R$ defined by $f (x) = \frac{x ^{2} - a x + 1}{x ^{2} + a x + 1}$ , $a \in (0, 2)$ .

Which of the following is true?

Options:

Answer:

Solution:

$ln (- 1, 1), f^{'} (x) = \frac{2 a ( x ^{2} - 1 )}{( x ^{2} + a x + 1 ) ^{2}} \Rightarrow f^{'} (x) = \frac{( + ) ( - )}{( + )} < 0$ $∴ f (x)$ is decreasing $f^{'} (x) = 0 \Rightarrow x^{2} - 1 = 0 \Rightarrow x = 1, - 1$ $∴ f^{''} (1) = \frac{4 a}{( 2 + a ) ^{2}} > 0$ $∴ f (x)$ has local minimum at $x = 1$ .

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

⏱ 2mℹ️ Source: QB

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