y = 3/ ³√x --function's equation

y= 3x ^ (-1/3)

Slope of function = dy/dx =m= 3(-1/3)x^ (-1/3 -1)

=> dy/dx = m= -x^ (-4/3) which = -1 / ∛x⁴

Rewrite x +16y +3 = 0 in the form y = mx +c where m is the slope of the line

=> 16y = -x -3

=> y = (-1/16)x - (3/16)

Therefore , m = -1/16

Since function and tangent are parallel , their slopes(m) are the same

=>-x^ (-4/3) = - 1/ 16

Cube both sides

=> [ -x^ (-4/3) ] ³ = (-1/16)³

=> [ -x^ (-4/3 x 3) ] = -1³/16³

=> -x⁻ ⁴ = -1 / 16³

=> x⁻ ⁴ = 16 ⁻³

=> 1/ x ⁴ = 1 / 16³

=> x⁴ = 16³

=> x = ±16 ^ ( 3 x 1/4)

=> x= ±16 ^ (3/4)

=> x=± 2^ (4 x 3/4)

=> x= ±2³

=> x=± 8

Solution : x= 8 , x= -8

16y = - x - 3

y = - x/16 - 3/16

The slope of the tangent line is -1/16

The slope of any function is the differential of y or y'

y = 3* (x)^{-1/3}

y' = {-1/3} 3 x ^{-4/3}

y' = -x^{-4/3}

{-1/16} = -x^{-4/3}

Now turn this over and divide by - 1

16 = x^{4/3}

16^{3/4} = x^{4/3*3/4}

8 = x

x can also be - 8 because (16)^{1/4} = - 2

-2^3 = - 8