Consider the polynomial (x) = −0.1x 4 − 0.15x 3 − 0.5x 2 − 0.25x + 1.2 The true value of its derivative at x=0.5 is ′ (0.5) = −0.9125. Use backward, forward, and centered first finite differences to estimate the derivative numerically for the step size ∆x = 0.25, and determine the percent error between the true value and each of the estimated values (percent error is given by = − mconverted to a percentage.) What value of ∆x would you have to use for the backward and forward finite differences to get the same percent error as the centered finite difference (hint: it should be less than 0.25.)?

Mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.