Equation of a curve and finding the value of k.

Apr 2010
Reading, Berkshire.
Hello, can anyone help me how to find the value of k? I keep getting the wrong answer. I got 4.4 but the correct answer is 9. Here's the question:

The equation of a curve is y=3x^2-kx+2, where k is a constant. The tangent to the curve at the point where x=2 passes through (5,5). Find the value of k.

That's the question.

I did my working like this.. Firstly, I have to find the tangent which I got 12-k. Then I tried to solve everything. I put the coordinates into the equation of a curve.. Which gives me the value of k but I got 4.4 :S
Oct 2008
Hopefully you sketched a graph, though?

There's a formula for the equation, and what it does is set m = the derivative at x = 2 (i.e. m = 12 - k, as you say) and then it says (but you could tell this from a sketch - of ANY curve, in fact) that the y-intercept,

c = y(2) - 2m = 14 - 2k - 24 + 2k = -10.

So you have a c to plug into

5 = m*5 + c = (12 - k)*5 + c

and you can solve for k.