find the function f(x) the graph passes through (1,2) and whose tangent line at the point (x,F(x)) has a slope of 1/x3
Suppose (x,y) is any point on this curve. Then, since (1,2) is also on this curve, the tangent of the curve is,
You could simplify the expression as you wish(eg; take y=f(x) if you want) to get the equation of the curve.
Hope this will help you.
It's because, when we integrate, we must calculate the new power
before dividing by it.
and when we differentiate, we multiply by the original power
before reducing the power by 1.
yes, with the curve, only the point of tangency is on the line
in that vicinity.