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MathNet 2021 — Part 08 Question 52

Math Olympiad Vault · MathNet 2021 — Part 08

Question 52

At which points on the curve $f(x)=x^3-2x^2+3$ does the tangent have inclination $135^\circ$ to the $x$-axis?
  1. $T_1(1,-4)$ and $T_2(-2,0)$.
  2. $T_1(1,-4)$ and $T_2(2,0)$.
  3. $T_1(1,0)$ and $T_2(-1,4)$.
  4. $T_1(1,2)$ and $T_2\left(\frac13,\frac{28}9\right)$.
  5. $T_1(1,2)$ and $T_2\left(\frac13,\frac{76}{27}\right)$.