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Geometry Level 3

What is the shortest distance of ( 0 , 0 ) (0,0) from the curve y = e 2 x + e − 2 x 4 y = \dfrac{e^{2x} + e^{-2x}}{4} ?

3 2 \dfrac{3}{2} 1 2 \dfrac{1}{2} None of these 1 1 2 2

Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Aqid Khatkhatay
Dec 27, 2016

The expression is coshx/2 y=(1/2)coshx dy/dx=(1/2)sinhx For function to be max or min dy/dx=0 So x=0 d2y/dx2=1/2 therefore function is minimum Now y=1/2 at x=0 so point is (0,1/2) So distance is 1/2 units

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