Could you please help me with this question:

Question

Determine the values of x so that the tangent to the function (y=3/cubic root of x) is parallel to the line x+16y+3=0

Thank you

Answer 1

(1) Get the slope of the line x+16y+3=0
It will help if you rewrite it as
y = -x/16 - 3/16

(2) require that the slope of the function
y = 3/x^(1/3).
which is dy/dx = -1/x^(4/3)

equal the slope value from (1). Solve for x.

Answer 2

Thank you drwls,

But how do I equate the two equations?

I know the answer is 8, but I can't solve it properly.