Homework question for class SIE 270. Two point formula not included: f^(1)(x)=((f(x+h)-f(x))/h)

4 . Let ( ( x) = ex + 2 x + 3. Apply the two, and three - point formulas of tables 4.3 ( given below ) to estimate derivatives of f ( x ) at xo = 0. Use two step size h = 10 - 1 and 1 = 10 - 2 . find actual error by comparison with the analytical derivatives . TABLE 4. 3 Some Popular Derivative Approximations First derivative approximations Three - point f " ( * ) = * (* + h ) - f (* - 1 ) + 0 ( 1 2 ) Four - point f' (* ) = - } ( * + 2 h ) + 6 f ( * + h ) - 3f (* ) - 24 (* - 12 ) + 0 ( 1 3 ) 49 Five - point f ' ( x ) = - 27 ( * + 2. h ) + 16 f (* + h ) - 16f (x - } ) + 27 (* - 212 ) + 0 ( 1 4 ) 24 h Second derivative approximations Three - point f " (* ) = * ( * + 12 ) - 2 f (* ) + f (* - 12 ) + 0 ( 1 2 ) h ? Four - point Coincides with three - point formula Five - point f " ( X ) = - * (* + 2.12 ) + 16 f (* + h ) - 30 * (* ) + 16f (x - } ) - flox - 212 ) 12 / 2