Use the most accurate Three Point Formula to determine each

Use the most accurate Three- Point Formula to determine each missing entry in the following tables.

Solution

For table1:

f\'(-0.2) = ( f(-0.1) - f(-0.3) )/( 2*0.1 ) = -0.595

f\'(-0.1) = ( f(0) - f( -0.2 ) )/ 0.2 = 1.22

Similarly you can find for other tables using the fact that :

f\'( x ) is approximately equal to    [ f(x+h) - f(x-h) ] / [ 2*h ]