Question

popcorn while using less paper to manufacture them. il l suript can help manufacturers of popcorn tubs to optimize it to carry Q5. The polynomial y is defined as (20 points) y 2 x4-7 x3- 44 x92.5 x262.5 (a) In a script file, Initials_MT_Pb_05.m, define y using an anonymous function. (b) Use the anonymous function to evaluate y when x-3, x-0, x-3. (c) Use the anonymous function handle to plot y for-4sxS 5.5 Hint: Use fplot. (d) Use the plot you generated in part (c) to get an estimate of the location of zeros then use proper command to find the exact location of all the zeros of the anonymous function ha x01 (e) Use the plot you generated in part (c) to get an estimate of the location of the minimums proper function to find the 2 minimum values of y and the corresponding x values. [xminl, yminl]-

Answer 1

Please find required MATLAB code along with necessary details in comments:

clear all; % clear workspace
close all; % close all figures
clc % clear command window

%% define anonymus function
y=@(x) (2*x^4) -(7*x^3) -(44*x^2) + 92.5*x +262.5;

%% evalaute function value at x=-3, 0, 3
y_n3=y(-3)
y_0=y(0)
y_3=y(3)

%% plot the function
h1=fplot(y,[-4,5.5]);  
grid on;
hold on
h2=fplot(0); % plot x-axis

%% locate all zeros in the function plot using initial estimates
% obtained from the graphs

% x = fzero(fun,x0) tries to find a point x where fun(x) = 0. This solution
% is where fun(x) changes sign—fzero cannot find a root of a function such as x^2.

x01=fzero(y,-4)
x02=fzero(y,-2)
x03=fzero(y,4)
x04=fzero(y,5)

% plot the zeros for ease of reference
h3=plot([x01;x02;x03;x04],[0;0;0;0],'r*');

%% Locate the minimum of function value from the estmates obtained from the
% graph

% x = fminsearch(fun,x0) starts at the point x0 and attempts to find a
% local minimum x of the function described in fun.

[xmin1,ymin1] = fminsearch(y,-3)
[xmin2,ymin2] = fminsearch(y,5)

% plot the minimum for ease of reference
h4=plot([xmin1;xmin2],[ymin1;ymin2],'bs');
legend([h1,h2,h3,h4],{'y(x)','x-axis','Zeros','Local Minima'});

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