Solved: Investigation Consider the function (a) Write a short paragraph giving a
Chapter 5, Problem 69(choose chapter or problem)
Consider the function
\(F(x)=\frac{1}{2} \int_{x}^{x+2} \frac{2}{t^{2}+1} d t\)
(a) Write a short paragraph giving a geometric interpretation of the function F(x) relative to the function
\(f(x)=\frac{2}{x^{2}+1}\).
Use what you have written to guess the value of x that will make F maximum.
(b) Perform the specified integration to find an alternative form of F(x). Use calculus to locate the value of x that will make F maximum and compare the result with your guess in part (a).
Text Transcription:
F(x)=frac 1 2 int_x^x+2 frac 2 t^2+1 d t
f(x)=frac 2 x^2+1
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