Let Curve C be f(x)=(1/3)(x^2)+8 and line L be y=3x+k where k is a positive constant. Given that L is tangent to C, find the value of k. (6 marks approx)

SO when we see the word tangent we should be thinking about rate of change. Recall that the line being a tangent means they meet and have the same derivative at this point OR we find k such that f(x)-y=0 has a double root. (We can prove that this is true!)So(1/3)x^2+8-k-3x=0 so we solve for k such that the discriminant is 0. that is 9-4(1/3)(8-k)=0 This implies k=8-27/4=5/4