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04-2: Monotonic transformation and the gradient vector Consider a function f : R" ) IR. Let h be a (weakly) increasing function, and g(a:) =

5) May you help with an explanation to understand the following practice problem:

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04-2: Monotonic transformation and the gradient vector Consider a function f : R“ —) IR. Let h be a (weakly) increasing function, and g(a:) = h[f(a:)). Now suppose both f, hare continuously differentiable.
Take an arbitrary interior point .113&quot; What is the relationship between Vﬂm‘) and Vg(:* }? (Notice that they are both vectors. Having this in mind.)
1. Can they &quot;point to&quot; different directions? 2. Can they have different &quot;size&quot;?

1 . No, if we ignore the bad... View the full answer

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