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.

Solutions

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,
Keep posting questions.

milcah answered 1 year ago

Next > < Previous

Related Solutions

write a function to determine the square root of a number. The square root of a...

write a function to determine the square root of a number. The square root of a number can be approximated by repeated calculation using the formula NG = 0.5(LG + N/LG) where NG stands for the next guess and LG stands for the last guess. The loop should repeat until the difference between NG and LG is less than 0.00001. Use an initial guess of 1.0. Write a driver program to test your square root function. I WANT THIS PROGRAM...

prove that positive operators have unique positive square root

Babylonian Algorithm. The Babylonian algorithm to compute the square root of a positive number n is as follows:

Chapter 3 Exercise 1Babylonian Algorithm. The Babylonian algorithm to compute the square root of a positive number n is as follows: 1. Make a guess at the answer (you can pick n/2 as your initial guess). 2. Computer = n / guess. 3. Set guess = (guess +r) / 2. 4. Go back to step 2 until the last two guess values are within 1% of each other.Write a program that inputs an integer for n, iterates through the Babylonian algorithm until the guess...

Match each table with its equation. OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal Input...

Match each table with its equation. OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal Input Output -2 -8 -1 -1 0 0 1 1 2 8 3 27 OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal Input Output -2 _ -1 _ 0 0 1 1 4 2 9 3 OPTIONS -Linear, Square Root, Quadratic, Absolute Value, Cubic, Reciprocal Input Output -2 -0.5 -1 -1 0 _ 1 1 2 0.5 3 0.33 OPTIONS -Linear, Square Root, Quadratic,...

Deduce from the Completeness Axiom that there exists a square root of a real number a...

Deduce from the Completeness Axiom that there exists a square root of a real number a if and only if a ≥ 0

4. Use a proof by contradiction to show that the square root of 3 is irrational....

4. Use a proof by contradiction to show that the square root of 3 is irrational. You may use the following fact: For any integer k, if k2 is a multiple of 3, then k is a multiple of 3. Hint: The proof is very similar to the proof that √2 is irrational. 5. Use a direct proof to show that the product of a rational number and an integer must be a rational number. 6. Use a proof by...

Write three functions that compute the square root of an argument x using three different methods....

Write three functions that compute the square root of an argument x using three different methods. The methods are increasingly sophisticated, and increasingly efficient. The square root of a real number x is the value s such that s*s == x. For us, the values will be double precision variables and so may not be perfectly accurate. Also, for us, assume that x is in the range 0.0 to 100.0. You program should have a main() that asks the user...

Use the slope of the graph of τ vs. square root of L to calculate g...

Use the slope of the graph of τ vs. square root of L to calculate g and its uncertainty. δg = 2g δ (slope) Show your work we should use m2=2buy/sqrtof y but how?!! http://www.pa.msu.edu/courses/2015summer/PHY251/labfiles/practical2.pdf

Use calculus to find three positive numbers that sum to 150 with the greatest possible product.

Determine the positive real root of ln(x^2)=0.8 by the following methods. (Note that you need to...

Determine the positive real root of ln(x^2)=0.8 by the following methods. (Note that you need to show the details of your derivations in MATLAB). a) Graphically ( plot the function and copy your figure to word). b) Using two iterations of the bisection method with initial guesses of xl=0.4 and xu=2 and populate the following table. What is the root after two iterations? Provide justification for the values you have obtained in your MATLAB code as comments. i xl xu...

Subjects