1. ## calculus/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

2. Originally Posted by sxusteven
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
At x = -4 the gradient of the tangent is to the curve is -8a. So your line has to have this gradient ......

Also, at x = -4, y = 16a. So the point (-4, 16a) lies on the curve and hence must also lie on the line .....

3. Originally Posted by sxusteven
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 $y=-2x+b$

The slope of this line is $-2$

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

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

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

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

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

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

Then solve for b.

Can you take it from here?

--Chris