Check my work:
At what value of x does the function 1/(1+x^2) change from increasing to decreasing?
I'm not sure what I did, but I think it's right.
My work: Derivative 1/(1+x^2) -> -2x/(1+x^2)^2 = 0. Solving for x gives 0. Therefore, the answer is zero.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
the answer is 1....x^2 is always positive, so 1+x^2 will have a minimum value of 0 (which is unacceptable as u cant divide anything by 0)....again, 1/1+x^2 will have maximum value 1 when x=0, so, the graph will ascend upto 1 and then start descending.
Though your answer is right, but still you'll have to confirm if that is maxima ( goes from increasing to decreasing)
For that, you'll have to find the 2nd derivative and check if it is positive or negative for x=0
If it is negative, then it is a maxima, otherwise not.
2nd derivative ->(6x^2 -2)/(1 + x^2)^3
for x=0 , it is negative,which justifies your answer.
I'm not sure what I did. Did I find the inflection point?
Not the answer you are looking for? Search for more explanations.
my bad, i didnt notice the 'what value of x' part....u r right, it's 0.
That'd have been an inflection point only if second derivative of f(x) had come equal to 0 for x=0
but 2nd derivative is -2 i.e. negative here, hence it is not an infection point but is a maxima, where your function goes from increasing to deceasing.