given

and

I know the derivatives are and

how are the equations of 2 tangent lines found to both graphs

the answers are: and

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- Feb 6th 2010, 10:31 AMbigwavefind tangent lines
given

and

I know the derivatives are and

how are the equations of 2 tangent lines found to both graphs

the answers are: and - Feb 6th 2010, 11:08 AMrunning-gag
- Feb 6th 2010, 11:12 AMearboth
1. You have the parabolas:

and

2. Let P(p, p²) denote the tangent point on the parabola p and Q(q, -q²+6q-5) the tangent point on the parabola q.

3. The tangent to p at P has the equation:

and the tangent to q at Q has the equation

4. Both equations describe the same line. Thus

5. Solve this system of simultaneous equations for p and q. Resubstitute the result into the equations of and .

6. For confirmation: Draw the 2 parabolas and the tangents. - Feb 6th 2010, 02:24 PMbigwave
- Feb 7th 2010, 01:21 AMHallsofIvy
Here's a tip- in the future tell us what the problem

**really**says! Here, you have never said exactly which tangent lines you want to find. Every graph has an infinite number of tangent lines.

I**suspect**that the problem is asking for lines that at tangent to**both**of these graphs. Suppose y= mx+ b is the equation of such a tangent line. At the point, where that line is tangent to we must have and . At the point, where it is tangent to , we must have and so we have 4 equations to solve for m, b, , and - Feb 7th 2010, 08:12 PMbigwave
yes the 2 tangent lines would be tangent to both graphs.

it was baffeling to determine the slope of the 2 lines just based on the derivatives and not knowing the points of contact..

appreciate the replys