[TomFoolery]

Consider the function plotted in blue above:

y = 0.5x2 - x - 1.5


Using the rules of calculus, the derived function is:

dy/dx = 2×0.5x^2-1 - 1×x^1-1 - 0

= x - 1


For any 'x' value, the 'y' value of the derived function equals the gradient of a tangent to the original function at that point.