suppose y=-2x^2(x+4) for what values of x does dy/dx=10

Question

I just need help on setting up the problem, Do I need to use the product rule?

Answer 1

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