If the line y - 8x = -2 is tangent to the curve y = 2/3x^3 + c, find at least one value for c.

Answer 1

y=8x-2 has slope =8

y' = 2x^2 = 8 when x = plus or minus 2

y=8(2)-2 = 14

14 = (2/3)(2)^3 + c

14- 16/3 = c

26/3 = c