When x=1 f(1)=e^-1=1/e. Derivative of f is e^(-x^2)-2x^2e^(-x^2). When x=1 f'(1)=-1/e. If we write f'(x) as dy/dx then at x=1, dy=-dx/e. If dx=-0.1 then dy=0.1/e, implying that f(1-0.1)=f(0.9) approx equals f(1)+dy=1/e+dx=1/e+0.1/e=0.37+0.037=0.41. To one place of decimals f(0.9)=0.4.