suppose y=-2x^2(x+4) for what values of x does dy/dx=10
Yes, use the product rule, which is ...
y = uv
dy/dx = u.(dv/dx) + v.(du/dx)
we have
y = -2x^2(x + 4)
dy/dx = (-2x^2)(1) + (x + 4)(-4x)
dy/dx = -2x^2 - 4x^2 - 16x
dy/dx = -6x^2 - 16x
Setting dy/dx = 10,
-6x^2 - 16x = 10
6x^2 + 16x + 10 = 0
3x^2 + 8x + 5 = 0
(3x + 5)(x + 1) = 0
x = -5/3, x = -1