1. ## solving equation

is the point on the curve where .
The tangent to the curve at has equation .
What is the value of ?

but so far i have done

$\displaystyle \frac{dy}{dx} = 2x - 1$

$\displaystyle y = -6x-5$

where do I go from here?

equation both equations?

I get $\displaystyle 2x-2 = -6x-5$

I dont know what to do? Any help appreciated

2. ## Re: solving equation

Can I suggest that you try to keep clear in your mind that those two y's are not the same function.
You have two functions here, so let me given them separate names, f and l (for "line").

$\displaystyle f(x) = x^2 - x + 5$, and $\displaystyle l(x) = -6x - 5$.

Thus I'd translate the problem like this:

"Let the point $\displaystyle P = (k, f(k))$. Suppose the tangent line to $\displaystyle f$ at $\displaystyle P$ (i.e. at $\displaystyle x = k$) is $\displaystyle l$. Find $\displaystyle k$."

When I taught Calculus I, I think the phrase I repeated more than any other was "the derivative is the slope of the tangent line." When you take Calculus I, you should make sure that you deeply, completely, and unforgettably understand it. It's a central, vital concept.