For every pair of continuous functions f , g : 0 , 1 → R such that max ⁡ f x : x ∈ 0 , 1 = max ⁡ { g x : x ∈ 0 , 1 } , then the correct statement (s) is (are)

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryMiscellaneous/MixedHard2 minPYQ_2014

MathematicsHardmultiple choice

For every pair of continuous functions $f, g : [0, 1] \to R$ such that $\max \{f (x) : x \in [0, 1]\} = \max {g (x) : x \in [0, 1]},$ then the correct statement (s) is (are)

Options:(select one or more)

Answer:

A, D

Solution:

Let $f (x)$ and $g (x)$ achieve their maximum value at $x_{1}$ and $x_{2}$ respectively
$h (x) = f (x) - g (x)$
$h (x_{1}) = f (x_{1}) - g (x_{1}) \geq 0$
$h (x_{2}) = f (x_{2}) - g (x_{2}) \leq 0$
$\Rightarrow$ $h (c) = 0$ where $c \in [0, 1] \Rightarrow f (c) = g (c) .$

Stream:JEE_ADVSubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2014

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