Theory test: Derivatives and gradients

6 questions. Pass with 5 correct.

1. 01 What is the derivative of $f(x)=3x^2+2x$ at $x=1$?

   5683
2. 02 What is the gradient of $f(x,y)=x^2+3y$ at the point $(2,1)$?

   $(4,3)$$(2,3)$$(4,1)$$(7,7)$
3. 03 During gradient descent the loss jumps around and then grows without limit. The most likely cause is:

   The learning rate is too smallThe learning rate is too largeThe gradient is zeroThere are too many training examples
4. 04 For $y=(2x+1{)}^3$, what is $dy/dx$ at $x=0$?

   3261
5. 05 The negative gradient $-\nabla L$ points in the direction of:

   Steepest increase of $L$Steepest decrease of $L$Along a contour line (no change)The global minimum, always
6. 06 A variable $x$ is used in two places in a computation. Its gradient is:

   The gradient from the first use onlyThe product of the gradients from both usesThe sum of the gradients from both usesThe larger of the two