# Differentiation Question help

1. May 24, 2010

### jaycool1995

1. The problem statement, all variables and given/known data
The curve C has equation $$y=k x^3-x^2+x-5$$ where k is a constant.

A) Find the derivative of the function with respect to x

The point A with x-coordinate $$-\frac{1}{2}$$ lies on C. The tangent to C at A is parallel to the line with equation $$2 y-7 x+1=0$$ .

Find...

B) the value of k

C) the value of the y-coordinate at A.

2. Relevant equations

C is $$y=k x^3-x^2+x-5$$
Equation of the line parallel to the tangent of C at A ( $$-\frac{1}{2}$$) $$2 y-7 x+1=0$$ .

3. The attempt at a solution

Ok, so I have found the derivative to be equal to: $$y'=3 k x^2-2 x+1$$

I am having trouble with the find y (and k) because if you were to solve that equation by substituting into it x we then have: $$\frac{1}{2} (7 x-1)=y=-2.25$$ but that y value isn't on the tangent line to C. So how would i go about completing these problems?

Thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 24, 2010