Math Help - Tangent

1. Tangent

Show that the tangent to the curve y=(x^2+x-2)^3 +3 at the point (1,3) is also tangent to the curve at another point.

Just a question about how I get the answer to this question.. is this method correct?
I find the derivative of y. Then find the equation of the tangent at x=1. Make the equation of the tangent at x=1 equal to the original function. Solve for x.

2. Originally Posted by skeske1234
Show that the tangent to the curve y=(x^2+x-2)^3 +3 at the point (1,3) is also tangent to the curve at another point.

Just a question about how I get the answer to this question.. is this method correct?
I find the derivative of y. Then find the equation of the tangent at x=1. Make the equation of the tangent at x=1 equal to the original function. Solve for x.
Close.

Find the derivative.

Evaluate the derivative at $x = 1$.

Once you have found this, put what you have just evaluated equal to the DERIVATIVE function.

Then solve for $x$.

3. Uh, Prove It, what skeske1234 did, find the equation of the tangent line and see if it intersects the curve at another point, is correct.

What you are doing will only determine if there is another point at which the slope of the tangent line is the same- the two tangent lines may be parallel, but not the same line

4. On the other hand, unless you ALSO do what Prove It suggests, you won't know that your second intersection finds the line tangent to the curve.