Consider the function which maps a vector to its maximum entry, ↦ maxᵢ ᵢ. While this function is non-smooth, a common trick in machine learning is to use a smooth approximation, LogSumExp, defined as follows.
LSE : R" → R, LSE(x) = ln » R, LSE(P) = ln [ (i=1) Σ eˣᶦ]
One of the nice properties of this function is that it is convex, which can be proved by showing its Hessian matrix is positive semidefinite.
To that end, compute its gradient and Hessian.

an altitude of 15,000 feet

step-by-step explanation:

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.