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Higher Derivatives. If f is differentiable to f’ , then f’ may have its own derivative, f’’ , called the second derivative This is the rate of change in f’ – how fast f’ is changing. Example. If , find f’’. More.

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Presentation Transcript
slide2

If f is differentiable to f’, then f’ may have its own derivative, f’’, called the second derivative

  • This is the rate of change in f’ – how fast f’ is changing
example
Example

If , find f’’

slide4
More

Derivative of f’’ is f’’’ – Third Derivative

Derivative of f’’’ is f’’’’ – Fourth Derivative

Etc.

example1
Example

Find y’’’’ or y(4)of

example2
Example

Find D(27)of y = cos x

acceleration
Acceleration
  • Velocity is how fast distance is changing (f’)
  • Acceleration is how fast velocity is changing (f’’)
  • A particle’s position is given by the function

, find its acceleration at 4.0 sec.

Graph the position, velocity, and acceleration functions and explain.