Create the following function in matlab fx x2 05ex 4 Eval

Create the following function in matlab: f(x) = x^2 = 0.5e^-x - 4 Evaluate the values of function between the interval -2 lessthanorequalto x lessthanorequalto 6. Select a step size of 0.1 and plot the function. How many zeros does this function have? Use f zero to find the location of zero(s) of the function. Find the minimum value of the function and its location between the interval -1 lessthanorequalto x lessthanorequalto 5.

Solution

func.m (This function evaluates the value of the given function at a value of x)

function f = func(x)

f = power(x,2) + exp(-1*x) - 4; %returning the value of the function

script.m (This file is where everything happens)

fun = @func; %imports func as fun
fs = zeros(81); %creates an array to store the values of function at different xs between -2 and 6
xs = zeros(81);
min = 1000000; %initialization of minimum
for i = -2:0.1:6 %looping through -2 to 6 with an interval of 0.1
    f = func(i);
    fs(int32((i+2)*10+1)) = f;
    xs(int32((i+2)*10+1)) = i;
    if (i>=-1 & i<=5 & f<min)
        min = f; %updating minimum
    end
end

x0 = [-1 2];
plot(xs, fs); %plotting xs and fs at various values
zeros = fzero(fun, x0); %finding zeros of the function
disp(zeros); %dispplaying zeros
disp(min); %displaying minimum