Minima maxima: Arbitrary constants for a cubic

Submitted by Francis June E… on

Make the curve y=ax³+bx²+cx+d pass through the points (0,1)and (-3,7) and have a critical point at (-1,3)

Ans. y=-x³-4x²-5x+1
Thanks po

Tags
Minima maxima

Jhun Vert Mon, 04/13/2020 - 10:52

Steps:

  1. Substitute (0, 1) to the equation.
    Result: d = 1.
  2. Substitute (-3, 7) to the equation.
    Result: -27a + 9b - 3c = 6.
  3. Substitute (-1, 3) to the equation.
    Result: -a + b - c = 2.
  4. Differentiate and set y' to zero. Because (-1, 3) is a critical point, replace x with -1.
    Result: 3a - 2b + c = 0.
  5. Solve the three equations from steps (2), (3), and (4).