y = (x + 4) * (x^2 - 5x)
y = x^3 + 4x^2 - 5x^2 - 20x
y = x^3 - x^2 - 20x
dy/dx = 3x^2 - 2x - 20
Setting dy/dx to zero, we have:
3x^2 - 2x - 20 = 0
Using the quadratic formula, we will get:
x = [2 +/- sqrt((-2)^2 - 4(3)(-20))] / [(2)(3)]
x = [2 +/- sqrt(244)] / 6
x = 2.936749892 or x = -2.270083225
x = 2.9 or x = -2.3 [1 decimal place]
When x = 2.936749892,
y = (2.936749892)^3 - (2.936749892)^2 - 20(2.936749892)
y = -42.03149854
y = -42.0 (1 decimal place)
When x = -2.270083225,
y = (-2.270083225)^3 - (-2.270083225)^2 - 20(-2.270083225)
y = 28.55001705
y = 28.6 (1 decimal place)
dy/dx = 3x^2 - 2x - 20
d^2 y / dx^2 = 6x - 2
Setting d^2 y / dx^2 to zero, we have:
6x - 2 = 0
6x = 2
x = 0.333333333333...
x = 0.3 (1 decimal place)
When x = 0.333333..., we have:
y = (1/3)^3 - (1/3)^2 - 20(1/3)
y = -6.74074074....
y = -6.7 (1 decimal place)
Hence, we have:
p(2.9 , -42.0), p(-2.3 , 28.6), p(0.3 , -6.7)