Hi Candidate,

Local maximum and local minimum are the points of inflexion of the curve, which have maximum value at local maxima and minimum value at local minima at the curves.

In the function f(x) = 9x, so the value of f'(x)= 9, and the value of f''(x) = 0, which is the point of inflexion. At these values the curve attain the maxima/ minima values at those values.

Hope that this answer helps you, All The Best.

Have a Good Day!!