Find the constant kkk such that the function f(x)=kx2+1xf(x) = kx^2 + \frac{1}{x}f(x)=kx2+x1 has an inflection point at x=1x = 1x=1.
k=1k = 1k=1
k=1/2k = 1/2k=1/2
k=−1/2k = -1/2k=−1/2
k=−1k = -1k=−1