thanks!Quote:

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

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- Dec 27th 2009, 12:50 AMBabyMiloTangent to a curveQuote:

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

- Dec 27th 2009, 12:54 AMBabyMilo
do i dy/dx it? then dy/dx=0

then sub x into

http://www.mathhelpforum.com/math-he...23de3734-1.gif

to get y.

then y=x+c

to find c?

thanks! - Dec 27th 2009, 12:58 AMProve It
If it is tangent to the curve, it will touch the curve only once.

Since they touch, they must be equal.

So

Since it only touches once, the discriminant must be 0.

So

. - Dec 27th 2009, 01:23 AMBabyMilo
- Dec 27th 2009, 02:20 AMHallsofIvy
This was posted in the "Pre Calculus" section so Prove It used a method that did not require the derivative.

Since you do mention the derivative, no, the derivative is not 0 where the line y= x+ c is tangent to it. A line is tangent to a curve where its**slope**is the same as the derivative. y= x+ c has slope 1 so you are looking for a place where the derivative is 1, not 0. - Dec 27th 2009, 03:43 AMBacterius
Here is a method using the derivative.

--------------------

The derivative of the function is (power rule on sum of functions).

The line has a slope equal to . Thus, you are looking for the point on the curve of where the slope is equal to . So, you must solve for . Hmm, .

Say (to make it less confusing). You know that*the tangent to the curve*of in a point of absciss is equal to :

Substitute :

That is : . Therefore .

:) - Dec 27th 2009, 05:11 AMHallsofIvy
- Dec 27th 2009, 12:51 PMBacterius
Ah, yes, I didn't spot that :)