gradient descent

Let xR be a real number, and f be a loss function on R. Then for a given point xnR, the value of our loss function will be f(xn). Gradient descent is given by xn+1=xnf(xn) for some learning parameter R. (i) Please check the following function is convex (you can do this with the second derivative): f(x)=e(2x)+4(x)e(x) (ii) Now perform Gradient Descent (this will be the 1-D case since our function is only in one variable) for 4 iterations on the function above to find the optimal point, starting with the initial condition x=5. (iii) Now optimize the function using the known first derivative test method. How far away (in absolute value) was gradient descent after 4 iterations from the true optimal point using the first derivative test method