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A positive number is added to the reciprocal of its square root. Use Calculus methods to...

A positive number is added to the reciprocal of its square root. Use Calculus methods to answer the following questions:what if anything, is the smallest such sum? What, if any, positive x-values will yield the smallest sum? Give exact answers as well as answers accurate to Five decimal place. Be sure to give a mathematical justification that you answer represents a minimum and not a maximum.

Expert Solution

Let x be that +ve number,

Then the function for the required sum is given by,

diff wrt x,

For critical points,

squaring,

Now find the second derivative to check if the critical point yields minimum sum,

diff wrt x,

The above value is +ve for any +ve value of x.

Hence the obtained critical point(positive number) yields minimum sum.

The minimum sum is given by,

I hope this answer helps,
Thanks,
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milcah answered 2 years ago

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