If the function `x^(2)-2kx + 3` is minimum at x=3 then find the value of k.

Explanation

Let`f(x) = x^(2) - 2kx +3`
` rArr f'(x) = 2x -2k`
For maxima or minima
`f'(x)= 0`
`rArr 2x-2k = 0`
`rArr k = x`
`rArr k= 3" "(.:' x=3)`
Now `f''(x) = 2 gt 0`
Therefore f(x) is minimum at x = 3
Thus k = 3.