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Tangent to a Cubic Graph

Directions: Use the digits 1-9, at most one time each, to fill the blanks.



Which numbers can be large? Which must be fairly small?



Two possible answers are:
The tangent to 𝑦=4𝑥^3−5𝑥^2+7𝑥 at the point (1, 6) is 𝑦=9𝑥−3
The tangent to 𝑦=3𝑥^3−4𝑥^2+6𝑥 at the point (1, 5) is 𝑦=7𝑥−2

There may well be others.

Source: Catriona Shearer

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