If the line - 4x+y=2 is tangent to the curve y=1/3x^3+c, find c

The slope of the line is 4. y = 4x + 2

The slope of the curve is y' = x^2

So when y' = 4, x^2 = 4 and x = + or - 2

c is irrelevant as it just raises or lowers the curve in a transformation mode.

Therefore c can be any real number.