solve in matlab"1. plot the graph of function f(x) = 0.1x 4 − x 2 − x + √ 7 + 2x with matlab, when −1 ≤ x ≤ 2. determine the maximum and minimum value of function f(x), when −1 ≤ x ≤ 2." in matlab

To solve this problem in MATLAB, you can follow these steps:

1. Define the function: Define the function f(x) as a MATLAB function. Here's how you can define the function:

main.m
f = @(x) 0.1 * x.^4 - x.^2 - x + sqrt(7) + 2 .* x;
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2. Define the range of x: Define the range of x values (-1 to 2) using the linspace function:

main.m
x = linspace(-1, 2, 100); % Generate 100 points between -1 and 2
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3. Plot the graph: Use the plot function to plot the graph of f(x) against x:

main.m
figure;
plot(x, f(x));
xlabel('x');
ylabel('f(x)');
title('Graph of f(x)');
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4. Find the maximum and minimum values: To find the maximum and minimum values of f(x), you can use the max and min functions:

main.m
max_value = max(f(x));
min_value = min(f(x));
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Here's the complete code:

main.m
f = @(x) 0.1 * x.^4 - x.^2 - x + sqrt(7) + 2 .* x;
x = linspace(-1, 2, 100);
figure;
plot(x, f(x));
xlabel('x');
ylabel('f(x)');
title('Graph of f(x)');
max_value = max(f(x));
min_value = min(f(x));
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Running this code will plot the graph of f(x) and display the maximum and minimum values of the function.