minimum distance between curves | Mathematics | Page 1

fickle hawk Jul 28, 2023, 2:06 PM

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Okay so I had this question which was to find the minimum distance between the curves y=3^x and y=logx with base 3
The first step our teacher told was that these functions are symmetric about y=x line because they are inverse functions so they will have a common tangent with slope 1 and hence we did the calculations by perpendicular distance and all
But I am confused as to why the common tangent required to find the minimum distance will be only that one and not anything else?
I forgot to ask him this. Please help

unreal sorrelBOT Jul 28, 2023, 2:06 PM

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fickle hawk Okay so I had this question which was to find the minimum distance between the c...

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gleaming sentinel Jul 28, 2023, 2:10 PM

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Screenshot_2023-07-28-19-40-18-38_40deb401b9ffe8e1df2f1cc5ba480b12.jpg

fickle hawk Jul 28, 2023, 2:11 PM

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Yes this is the exact thing we did

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But why did we take the slop of the curve's tangent as 1

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How do we know that it will be the minimum distance point

gleaming sentinel Jul 28, 2023, 2:12 PM

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fickle hawk But why did we take the slop of the curve's tangent as 1

please mark the thing you have a doubt as i coudnt understand your question

fickle hawk Jul 28, 2023, 2:13 PM

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gleaming sentinel

The 4th line

gleaming sentinel Jul 28, 2023, 2:18 PM

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fickle hawk The 4th line

if you visualize, you can observe line(y= x) to be a mirror and y= log3x is just the reflection of y = 3^x, and a reflection yields the same property as that of the of the object whose reflection is being formed

gleaming sentinel Jul 28, 2023, 2:19 PM

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gleaming sentinel if you visualize, you can observe line(y= x) to be a mirror and y= log3x is just...

this is just an informal concept for better understanding

fickle hawk Jul 28, 2023, 2:20 PM

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Ok thanks

fallow grail Jul 28, 2023, 4:13 PM

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serious