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.
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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?
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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.