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13B Higher Order Derivatives

Higher Order Derivatives

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13B Higher Order Derivatives

Higher Order Derivatives

Derivative f' y' D x  Leibniz

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EX 1 Find f'''(x) for f(x) = (3-5x)5 

notation notation notation notation

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13B Higher Order Derivatives

Ex 2 Find for .

Ex 3 What is ?

Ex 4 Find a formula for .

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13B Higher Order Derivatives

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 3-6t 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.

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13B Higher Order Derivatives