• Assume the function f is defined as f(x)=2.7cosx8.5sinxf(x)=2.7cosx8.5sinx
• Use the corresponding derivative rules to find the second derivative f(x)f(x) and evaluate that second derivative at x = 5.1. Be sure your calculator is in radians mode. Note: To avoid round-off error, retain at least eight decimal places in your calculations.
• Use the "central difference formula for the second derivative" to estimate f(x)f(x) at x = 5.1 for four different values of the mesh sizes
  • h = 0.2
  • h = 0.1
  • h = 0.05
  • h = 0.025
• Use your calculated values to fill in this table:

h	central difference approximation	exact second derivative	error = approximation - exact value
0.2
0.1
0.05
0.025

Note: To avoid round-off error, retain the maximum possible number of decimal places in calculations of the error.

• Answer the following two questions:
  • Does the error in the central difference approximation drop as the mesh size h is reduced?
  • As the mesh size h is reduced by a factor of 2, by what factor is the error in the central difference approximation reduced?