I'm reading through <http://ufldl.stanford.edu/tutorial/supervised/LinearRegression/>

[![enter image description here](https://i.stack.imgur.com/PBsTC.png)](https://i.stack.imgur.com/PBsTC.png)

How can I satisfy myself that the highlighted statement is true?

Can anyone Point me towards an intuitive understanding or visualisation?

PS Links:  

<https://en.wikipedia.org/wiki/Gradient#Differential_or_.28exterior.29_derivative> -- doesn't seem to help.  

[Gradient, tangents, planes, and steepest direction](https://math.stackexchange.com/questions/947604/gradient-tangents-planes-and-steepest-direction?rq=1)  

<https://en.wikipedia.org/wiki/Directional_derivative>