c) The slope of the tangent at P is the value of the first derivative at P. The slope is 2/3 which is a constant that is the same for all values of k. The equation can be found by substituting into y=mx+c the value for m and y and x that we know and solving for c. (7/27k)= (2/3)*(1/3k) + c therefore c is 1/27k and the equation is y=(2/3)x+ (1/27k)
The only part I really don't understand is B, but I included my work in case it would be helpful. I've tried to be as clear as possible, if anyone has ideas on how to make my math clearer, help is always appreciated. Hopefully somebody can explain this to me. The only thing I would ask is that the explanation is in terms suitable for the skills I've learned so far, as I am in high school. (IB HL if anyone knows what that is.)I assume it's a relatively simple thing since part b is only worth 2/13 points in the entire exercise. Thank you very much in advance for the help!