Practice question · Select all that apply
Select every statement that is TRUE of the gradient of a function of several variables.
Hints
- Four options restate the lesson's definition; one reverses a direction.
- Which way does gradient descent have to step, and why?
Show the answer
- A. At a smooth peak or trough, every partial derivative is zero at once.
- B. The gradient points in the direction of steepest decrease.
- D. A partial derivative treats every other variable as a constant.
- E. The gradient collects the partial derivatives into one vector.
Why
The gradient collects the partials, points uphill, has a magnitude giving the steepness, and vanishes at an extremum. It points towards steepest increase, so a minimiser must step the opposite way, the reason the algorithm is called gradient descent.
Practise Multivariable Calculus and Gradients
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