# solving equation

• Oct 8th 2012, 09:31 AM
Tweety
solving equation

The tangent to the curve at http://mapleta7.eps.surrey.ac.uk:808...ejlhffhhaf.gif has equation http://mapleta7.eps.surrey.ac.uk:808...nlkjhgcngp.gif.
What is the value of http://mapleta7.eps.surrey.ac.uk:808...bdhhmohaed.gif?

but so far i have done

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

$y = -6x-5$

where do I go from here?

equation both equations?

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

I dont know what to do? Any help appreciated

• Oct 8th 2012, 09:55 AM
johnsomeone
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").

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

Thus I'd translate the problem like this:

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

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.