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is strictly decreasing.
and is strictly decreasing on.
Hence, is strictly decreasing on.
It means that is strictly decreasing on.
It follows that is also strictly decreasing.
Since is strictly decreasing, we have.
on implies that is strictly decreasing on.
Then is strictly decreasing on and (4.7).
(b) (c) (d) is strictly decreasing.
Thus, f | [ a, b ] is strictly decreasing.
Therefore, ϕ ( u ′ ( t ) ) is strictly decreasing.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com