Question: Find the point on the curve y=x2+1 that is closest to the point (18,1).
Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot

All you need do is find the value for x that makes the numerator of the derivative equal to zero, in other words that satisfies the equation 2x^3 + x -18 = 0. In general solving a cubic equation can be difficult, but in this case it's pretty easy to guess the correct answer. Give it a try...