find the maximum slope of the tangent x/1+x^2 and also its points
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the slope of any curve/line is given by dy/dx where y is equal to that curve
so let y = x/1 = x^2 = x + x^2
therefore dy/dx = 1 +2x
i.e the slope of the tangent to the curve x/1 +x^2 is 1+2x
therefore as we increase the value of x the value of the slop increases
therefore when the x co-ordinate (x) is tending towards infinity the slope of the given curve is maximum
so let y = x/1 = x^2 = x + x^2
therefore dy/dx = 1 +2x
i.e the slope of the tangent to the curve x/1 +x^2 is 1+2x
therefore as we increase the value of x the value of the slop increases
therefore when the x co-ordinate (x) is tending towards infinity the slope of the given curve is maximum
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