Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationDifferentiation of composite functionsHard2 minPYQ_2014

MathematicsHardsingle choice

Let $f$ and $g$ be two differentiable functions on $R$ such that $f^{'} (x) > 0$ and $g^{'} (x) < 0$ for all $x \in R$ . Then for all $x$ :

Options:

Answer:

Solution:

Since $f^{'} (x) > 0$ and $g^{'} (x) < 0$ , therefore $f (x)$ is increasing function and $g (x)$ is decreasing function. $\Rightarrow f (x + 1) > f (x)$ and $g (x + 1) < g (x)$ $\Rightarrow g [f (x + 1)] < g [f (x)]$ and $f [g (x +$ 1) $] < f [g (x)]$ Hence option (b) is correct.

Stream:JEESubject:MathematicsTopic:DifferentiationSubtopic:Differentiation of composite functions

⏱ 2mℹ️ Source: PYQ_2014

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