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MathNet 2023-part-06 — 191 problems (EN–VI) Question 41

Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)

Question 41

Compute the coordinates of the intersection points of the graphs of the function $f(x)=x^{4}-2 x^{3}-7 x+2$ and the function $g(x)=3 x^{3}-8 x^{2}-1$. Write down the slope of the line through these two intersection points. Compute the tangent of the smaller of the angles between this line and the line with equation $3 x+2 y-11=0$.