Please help!

To simplify. let's assume that we're working with a uniform one-dimensional mesh. with the distance between adjacent nodes being the "mesh size" h. h Xi-1 Xi Xi+1 Thus, l | 3? + :3\" $i+1 and migl = my 7 h Knowing the value of a function fat each node in the mesh, your objective is to calculate the derivative of f at node X]. To derive the two formulas you'll be using. we start with the denition of the derivative: . IL' h, :r; fl(-'B):L1mh40f(+,llfll If we applied this formula to our grid values. we would get the forward difference expression NfIH 'fl's f,($i):l 11x) and the backward difference expression f I (xi) g fliilhflirxll Note that these are approximations to the value of the derivative, since we're not taking the limit as h goes to zero; but we can improve the approximation by taking the average of these two difference formulas: fl(mi) E %(f(1l7]i:f($xl + flmwl'flxkll) which simplies to the centered difference expression ll? from) flx'll)2}j(ma ll With this background. here's your assignment: - Assume the function f is defined as flx) : 5x4 - 9x3 + 2 . Use the power rule to nd the derivative f'(x) and evaluate that derivative at x = 1.7. MTG avoid round-off error. retain at least six decimal places in your calculations. . Use the "forward difference" and "centered difference" formulas to estimate f'(x) at x = 1.7 for three different values of the mesh sizes a l'l:0.1 n h=0.01 o h=0.001 Note: To avoid round-off error, retain at least six decimal places in yourfunctional evaluations, and retain the maximum possible number of decimal places in calculations of the forward and centered difference approximations. . Use your calculated values to ll in this table: Calculate derivatives using two finite difference formulas: forward difference centered difference _ _ h . _ _ . exact derivative apprOXImatIon apprommatlon 0.1 0.01 0.001 - Answer the following two questions: 0 Which formula yields a better approximation: The forward difference or the centered difference? 0 What effect does reducing the mesh size h have upon the accuracy of these approximations