Thread: 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

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 .....

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

The slope of this line is

Now, differentiate the function to get

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

Now when is ?

Once you have a, then plug the point into the function to find the value of the function at this point [which I will call ].

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

, where is the point on the function (and on the line)

Then solve for b.

Can you take it from here?

--Chris