Question:Find the value of the constant c for which the line is a tangent to the curve
Attempt:
NO IDEA
Well think about it. You are told that you are to find a line that is TANGENT to another line.
This means when the derivative of the second equation equals the slope of the first one:
and you want when it is equal to 2:
AND also you know that they both are equal at those x values. So you should be able to get two equations and solve them for C.
Not true.
Remember: is NOT , its !
So,
This gives us two functions of y:
and .
Now differentiate both and set both derivatives y' = 2. Only one of them will satisfy it and you'll get one value for x. This is the x coordinate of the tangent point. Find its y coordinate too and you'll get the tangent point. Plug this point in the line equation to get c.
A better approach is here:
If , then
Now set to get the tangent points y coordinate. This is much easier than working with two functions.