Second derivative - double check me please

[Becky4paws]

f(x) = 2x(x+4)^3

f'(x) = [(x+4)^3(2)] + [2x(3)(x+4)^2]
f'(x) = (x+4)^2(8x+8)

Assuming that is correct, the second derivative:

f"(x) = 8(x+4)^2 + 2(x+4)(x+1)
f"(x) = 8(x+4)[(x+4) + 2(x+1)]
f"(x) = 8x(x+4)(3x+6)
f"(x) = 24(x+1)(x+2)

I'm crossing my fingers, I think it may actually be correct

 

[galactus]

f(x) = 2x(x+4)^3

f'(x) = [(x+4)^3(2)] + [2x(3)(x+4)^2]
f'(x) = (x+4)^2(8x+8)

Assuming that is correct, the second derivative:

f"(x) = 8(x+4)^2 + 2(x+4)(x+1)
f"(x) = 8(x+4)[(x+4) + 2(x+1)]
f"(x) = 8x(x+4)(3x+6)
f"(x) = 24(x+1)(x+2)24(x+2)(x+4)

Now backtrack and see where you went wrong

I'm crossing my fingers, I think it may actually be correct