whats the point of double differentiation?

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double differentiation is used to find out if a curve has a maximum, inflection point or minimum.  It is also used to determine acceleration if you have a relationship between distance x travelled versus time t, e. g.,  x= f(t) = -2t^2 +4t +24.  f '(t) or the 1st derivative would provide the velocity dx/dt at time t, while the 2nd derivative f ''(t) would provide the acceleration at time t. dx/dt = -4t +4 d'x/dt = -4 hope this helps.