Consider a differentiable function {f}( {x}) on the set of real numbers such that {f}(-1)=0 and f^{'}(x)| \leq 2. Given these conditions, which one of the following inequalities is necessarily true for all x \in[-2,2] ?

Correct Answer is : f(x)≤2|x+1|

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 48 of 65

Marks: +1, -0

Consider a differentiable function

{f}( {x})

on the set of real numbers such that

{f}(-1)=0

and

f^{'}(x)| ≤ 2

. Given these conditions, which one of the following inequalities is necessarily true for all

x ∈[-2,2] ?

Solution:

{H}=\;{ {l}}/{2 π ρ} {ap}

For wire

ω_{1}

{H}_{1}=\;{l}/{2 π r}

For wire

ω_{2}

{H}_{2}=\;{2l}/{2 π 3 {r}}

Magnetic field will be circular and can be find out by right hand rule
Both fields will add at middle region

∴

at dotted line

{H}= {H}_{1}+ {H}_{2}

∴ {H}=\;{5 {l}}/{6 π {r}}

Now

{B}=µ {OH}

{B}=\;{µ_{0} 5l}/{6 π {r}}

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