The second order finite difference approximations of the first and second derivatives of f (x) are: flx + Ax) - flx Ax) f' (x) 24x f(x + Ax) + flx - Ax) 2f(x) f"(x) = Ax2
Consider the function f (x) cOS (x) Calculate the exact value of f' (x) atx = 1.5_ Calculate the exact value of f" (x) at x = 1.5. Calculate the approximate value of f' (x) at x = 1.5,for Ax = 0.1, 4x = 0.05, Ax 0.025. Calculate the approximate value of f" (x) at x = 1.5,for Ax = 0.1,Ax 0.05,Ax 0.025_