Given f(x) and deltaX, it follows that:

          f(x+deltaX) ≈ f(x) + <grad(f), deltaX> = f(x) + <grad(f), eps*grad(f)>

                                                                        = f(x) + eps|grad(f)|^2

                                                                        > f(x)

So, movement in the direction of grad always gives an increase value

Resources:

http://mathinsight.org/directional_derivative_gradient_introduction

http://mathinsight.org/directional_derivative_gradient_derivation