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Minimum and Maximum on an Interval (Extreme Values) Determine the vertex of y = x -6x +19. This function is in standard form. We need to complete the square to get it to vertex form. Show using algebra tiles and with algorithm. Method 1: Method 2: Therefore the vertex is ( , ). The minimum value of the function would be when x = The min./max. value is the y-portion of the vertex and where this min./max. occurs is the x-portion of the vertex. Calculus: Determine the max./min. value of f (x) = x2 -6x + 19 and state where it occurs. Since the min./max. value occurs at the vertex of the function which is a turning point, the slope of the tangent (ie: the derivative) will be zero. f '(x) = 0 at a maximum or minimum. Therefore, this is where it occurs, thusSo the maxJ'mirJ. occurs at x = 3 and is 10 but how do we find out whether it's a maximum or minimum without relying on previous parabola knowledge. Ie: leading coefficient is + or -. At a minimum, 1" '(x)