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The normal is perpendicular to the tangent at the point of contact, so its slope is the negative reciprocal −1/f'(a). Where the tangent is horizontal the normal becomes a vertical line.
Normal line
y = f(a) − (1/f'(a))(x − a)
The tangent slope is 6, so the normal slope is −1/6 and the line is y = −x/6 + 9.5.
The tangent is horizontal so the normal is the vertical line x = a, which has no gradient.