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if y increases as x increases
dy/dx will be positive
if y decreases as x increases
dy/dx will be negative
x= -b/2a
vertex of a parabola
dy/dx= 0
local maxima, local minima or stationary inflection

y=f’(a)(x-a) + f(a)
equation of the point with x-coordinate a
-1/f’(a)
gradient of the normal at x=a
y=-1/f’(a) (x-a) + f(a)
equation of the normal to the curve at x=a