1. y = x^3 - 5x^2 - x + 5
Let y = 0
0 = x^3 - 5x^2 - x + 5 = x^2(x-5) - (x - 5) = (x - 5)(x^2 - 1) = (x - 5)(x + 1)(x - 1)
Has solution : x = 5, x = -1, x = 1
x-intercept: (5, 0), (-1, 0), (1, 0)
Let x = 0
y = (0)^3 - 5(0)^2 - (0) + 5
y = 5
y-intercepts: (0, 5)
dy/dx = 0
dy/dx = 3x^2 - 10x - 1
0 = 3x^2 - 10x - 1
x = 3.45, x = 0
y = -16.9, y = 5
point: (5, 0, (-1, 0), (1, 0), (0, 5), (3.45, -16.90)
2. y = 27x^3 - 18x^2 - 48x + 32
Let y = 0
0 = 27x^3 - 18x^2 - 48x + 32 = 9x^2(3x - 2) - 16(3x - 2) = (9x^2 - 16)(3x - 2) = (3x - 4)(3x + 4)(3x - 2)
Has solution: x = 2/3, x = 4/3, x = -4/3
x-intercept: (2/3, 0), (4/3, 0), (-4/3, 0)
Let x = 0
y = 27(0)^3 - 18(0)^2 - 48(0) + 32
y = 32
y-intercept: (0, 32)
dy/dx = 0
dy/dx = 81x^2 - 36x - 48
0 = 81x^2 - 36x - 48
x = -0.60, x = 1
y = 48.50, y = -7
point: (2/3, 0), (4/3, 0), (-4/3, 0), (0, 32), (-0.60, 48,50), (1, -7)
