Question:Find the value of the constant c for which the line is a tangent to the curve

Attempt:

NO IDEA (Crying)

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- March 29th 2008, 12:28 PMlooi76[SOLVED] Differentiation Help!
**Question:**Find the value of the constant c for which the line is a tangent to the curve

**Attempt:**

NO IDEA (Crying) - March 29th 2008, 12:44 PMwingless
**Hint:**tells us the tangent lines slope is . So y' is 2 at the tangent point. - March 29th 2008, 12:46 PMTrevorP
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. - March 29th 2008, 01:50 PMwingless
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.