Homework Help: Doubts regarding gradient operator

1. Jul 26, 2014

utkarshakash

1. The problem statement, all variables and given/known data
I need some help regarding the gradient operator. I recently came across this statement while reading Griffith's Electrodynamics
"The gradient ∇T points in the direction of maximum increase of the function
T."

Wolfram Alpha also states that "The direction of ∇f is the orientation in which the directional derivative has the largest value and |∇f| is the value of that directional derivative. "

I'm finding it difficult to absorb this thing without any reasonable explanation. Can someone help?

2. Relevant equations

3. The attempt at a solution

2. Jul 26, 2014

vanhees71

Take a scalar field, $T(\vec{x})$ and calculate the directional derivative in direction of the unit vector $\vec{n}$ at a fixed point $\vec{x}=\vec{x}_0$. How is it related to the gradient? In which direction do have to choose $\vec{n}$ such that (modulus of) the directional derivative becomes maximal?

3. Jul 26, 2014

Infinitum

4. Jul 27, 2014