Limit of derivative to calculate derivative?

Question

f(x)= 2x^3+3x-5

 

 

Use the limit definition of the derivative to calculate the derivative of f:

 

f'(x)=

 

Use the same formula from above to calculate the derivative of this new function (i.e. the second derivative of f ):

 

f''(x)=

 

Answer 1

Use the difference quotient:

 

Find the limit of [f(x+h)-f(x)]/h  as h approaches 0. This will give you first derivative.

 

Find the limit of [f '(x+h)-f '(x)]/h  as h approaches 0.  This will give you the second derivative.