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
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