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 plot the graph of the function f(x) = 0.1x^4 − x^2 − x + √7 + 2x in MATLAB for the interval −1 ≤ x ≤ 2, you can follow these steps:

1. Define the function f(x) in MATLAB by creating a new file or function. Let's call it f.m. The file should contain the following code:

main.m
function y = f(x)
    y = 0.1 * x.^4 - x.^2 - x + sqrt(7) + 2 * x;
end
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2. In MATLAB, create a vector x for the range of values from −1 to 2. You can use the linspace function to evenly divide the interval:

main.m
x = linspace(-1, 2, 100); % 100 points from -1 to 2
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3. Evaluate the function f(x) for the vector x using element-wise operations in MATLAB:

main.m
y = f(x);
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4. Finally, plot the graph of the function using the plot function in MATLAB:

main.m
plot(x, y)
xlabel('x')
ylabel('f(x)')
title('Graph of f(x) = 0.1x^4 − x^2 − x + √7 + 2x')
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To determine the maximum and minimum values of the function f(x) for the interval −1 ≤ x ≤ 2, you can use the max and min functions in MATLAB:

main.m
max_value = max(y);
min_value = min(y);
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The variables max_value and min_value will then store the maximum and minimum values of the function f(x) within the given interval.