for what values of a and b is the line 2x+y=b tangent to the curve at y=ax^2 at x=-4

help would be welcome, thanks in advnace (Nod)

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- Oct 15th 2008, 08:53 PMsxustevencalculus/derivative question
for what values of a and b is the line 2x+y=b tangent to the curve at y=ax^2 at x=-4

help would be welcome, thanks in advnace (Nod)

- Oct 15th 2008, 08:56 PMmr fantastic
- Oct 15th 2008, 08:59 PMChris L T521
Rewrite the equation of the line as $\displaystyle y=-2x+b$

The slope of this line is $\displaystyle -2$

Now, differentiate the function $\displaystyle y=ax^2$to get $\displaystyle y'=2ax$

At x=-4, the value of the derivative is $\displaystyle -8a$.

Now when is $\displaystyle -2=-8a$?

Once you have a, then plug the point $\displaystyle x=-4$ into the function $\displaystyle y=ax^2$ to find the value of the function at this point [which I will call $\displaystyle y_0$].

Then, take this point and plug it into the equation for the line:

$\displaystyle (y_0)=-2(-4)+b$, where $\displaystyle (-4,y_0)$ is the point on the function (and on the line)

Then solve for b.

Can you take it from here?

--Chris