script that will calculate: roots, intercept on y axis, maxima and minima, the indefinite integral and the definite integral between -3 & 3. for g(t)=2t^2-3t-5 and f(x)=x^3-7x+6 in matlab

main.m
% define g(t) function
g_t = @(t) 2*t.^2 - 3*t - 5;

% define f(x) function
f_x = @(x) x.^3 - 7*x + 6;

% calculate roots of g(t)
roots_g_t = roots([2, -3, -5]);

% calculate intercept of g(t) on y-axis
intercept_g_t = g_t(0);

% calculate maxima and minima of g(t)
% first derivative of g(t)
g_t_prime = @(t) 4*t - 3;
% critical points of g(t)
critical_points_g_t = roots([4, -3]);
% second derivative of g(t)
g_t_second = @(t) 4;
% calculate maxima and minima based on second derivative
if g_t_second(critical_points_g_t(1)) > 0
    maxima_g_t = g_t(critical_points_g_t(1));
    minima_g_t = g_t(critical_points_g_t(2));
else
    maxima_g_t = g_t(critical_points_g_t(2));
    minima_g_t = g_t(critical_points_g_t(1));
end

% calculate indefinite integral of f(x)
indefinite_integral_f_x = @(x) 0.25*x.^4 - 3.5*x.^2 + 6*x + C; % where C is constant of integration

% calculate definite integral of f(x) between -3 and 3
definite_integral_f_x = integral(f_x, -3, 3);
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