Difference between "inflection" and "inflexion"?

Solution 1:

The -ction suffix for some terms of Latin origin ending in -xion was adopted especially in AmE from the 18th century. BrE spelling appears to prefer the -xion suffix:

Inflection (n.)

• also inflexion, early 15c., from Middle French inflexion and directly from Latin inflexionem (nominative inflexion) "a bending, inflection, modification," noun of action from past participle stem of inflectere "to bend in, to change" (see inflect). For spelling, see connection.

Connection:

• Spelling shifted from connexion to connection (especially in American English) mid-18c. under influence of connect, abetted by affection, direction, etc. See -xion.

-xion:

• ending favored in British English for certain words that in U.S. typically end in -ction, such as connexion, complexion, inflexion, as being more true to the Latin rules.

(Etymonline)

Solution 2:

In Jane Austin and Trollope for example, you always get 'connexion' which certainly looks archaic to an older (64) British reader such as myself (Family 'connexions' always loom large in early 19th century literature). However, the reason I am here just now is - I was using the word 'Inflexion' in a report. It sort-of looked right but I wasn't sure. Tried 'Inflection'; it looked right too. QED.