%var x y
def D(exprss):
    return exprss.derivative(x, 2)*exprss.derivative(y, 2) - (exprss.derivative(x, y))^2
@interact
def locextrema(f = input_box(default = x^2 + y^2, type = SR), critical_point = input_box(default = (0,0)), zoom = slider(-5, 5, 1, 0)):
    a = critical_point[0]
    b = critical_point[1]
    df(x,y) = factor(expand(f.derivative(x, x)))
    DD(x,y) = factor(expand(D(f)))
    fx(x,y) = f.derivative(x)
    fy(x,y) = f.derivative(y)
    fa = fx(a,b)
    fb = fy(a,b)
    html('<center>$f(x,y) = %s$</font></center>'%latex(f))
    html('<center>$f_{xx}(x,y) = %s$</font></center>'%latex(df(x,y)))
    html('<center> $D(x, y) = f_{xx}f_{yy} - (f_{xy})^2 = %s$ </center>'%latex(DD(x,y)))
    html('<center>$f_x (%s, %s)= %s, f_y(%s, %s)= %s $</center>'%(a, b, fa, a, b, fb))
    html('<center>$D(%s, %s) = %s, f_{xx}(%s, %s) = %s$ </center>'%(a, b, DD(a, b), a, b, df(a, b)))
    x_start = a -.5*2^zoom
    x_end = a + .5*2^zoom
    y_start = b - .5*2^zoom
    y_end = b + .5*2^zoom
    p = plot3d(f, (x, x_start, x_end), (y, y_start, y_end))
    show(p)