Homework SourseFind any relative extrema Need steps shown fxxx21 and gxxx21
f(x)=x/(x^2+1)
and
g(x)=x/(x^2-1)
Solution
Find any relative extrema. Need steps shown
f(x)=x/(x^2+1)
and
g(x)=x/(x^2-1)
Step 1. Take derivative.
f\'(x) = [(x2 + 1) - (x)(2x)] / (x2 + 1)2
g\'(x) = [(x2 - 1) - (x)(2x)] / (x2 - 1)2
Step 2. Set derivatives equal to 0 (so, f\'(x) = 0 and g\'(x) = 0).
f\'(x) = [(x2 + 1) - (x)(2x)] / (x2 + 1)2 = 0
g\'(x) = [(x2 - 1) - (x)(2x)] / (x2 - 1)2 = 0
Step 3. Solve for x-values
For f\'(x), x = -1 and 1
For g\'(x), x = -i and i (we will discard these solutions, as they are complex numbers)
Step 4. Plug them back in to the ORIGINAL EQUATION. The highest value is maxima; the lowerst is minima. Be sure to also test ±
f(-1) = -1/2
f(1) = 1/2
f(-) = approaches 0
f(+) = approaches 0
It\'s clear that our minima is at x = -1 and is f(-1) = -1/2
and our maxima is at x = 1, and is f(1) = 1/2
This function only has two extrema.
I hope that you found this answer useful towards your studies. It took a considerable amount of thought, time, and effort to compose, and and I\'d sincerely appreciate a lifesaver rating! It would really make my day, and will allow me to continue answering your questions :)
