Higher Order Derivatives, Schemes and Mind Maps of Differential Equations

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Higher Order Derivatives

Higher Order Derivatives Derivative f' y' Dx Leibniz First Second Third Fourth Fifth nth EX 1 Find f'''(x) for f(x) = ( 3 - 5 x)^5 notation notation notation notation

We know v(t) = s'(t) a(t) = v'(t) = s''(t) EX 5 An object moves along a horizontal coordinate line according to s(t)=t^3 - 6 t^2. s is the directed distance from the origin (in ft.) t is the time (in seconds.) a) What are v(t) and a(t)? b) When is the object moving to the right? c) When is it moving to the left? d) When is its acceleration negative? e) Draw a schematic diagram that shows the motion of the object.