a level maths

Find the possible values of c for which the line 24x+3y+c=0 is tangent to the curve f(x)=1/3x^3+9/x

tried finding the gradient of the tangent, but I'm not sure really how to approach the question, or what method to use

A tangent has the same value and derivative (at a point) as a function. So you have to find the points where the line is a tangent to the function and then find the y intercept c. A bit of looking ahead / sketch should get you thinking about where the line has the same gradient as the function, then think about how the values match.