The shortest distance of the point (0,0) from | vedclass

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(B) The given curve is $y = e^x + e^{-x}$.We want to find the shortest distance from the origin $(0,0)$ to this curve.Let $f(x) = e^x + e^{-x}$. By th

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$2$

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(B) The given curve is $y = e^x + e^{-x}$.We want to find the shortest distance from the origin $(0,0)$ to this curve.Let $f(x) = e^x + e^{-x}$. By the $AM$-$GM$ inequality,$e^x + e^{-x} \ge 2\sqrt{e^x \cdot e^{-x}} = 2\sqrt{1} = 2$.The minimum value of $y$ is $2$,which occurs at $x = 0$.Thus,the point on the curve closest to the origin is $(0,2)$.The distance between $(0,0)$ and $(0,2)$ is $\sqrt{(0-0)^2 + (2-0)^2} = \sqrt{4} = 2$.

The shortest distance of the point $(0,0)$ from the curve $y = e^x + e^{-x}$ is-

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