Quick Help?

[WTF?]

Hi, I got several Q's, so thanks for any input.

1) f(x) = 2 - x² and g(x) = 5 + x²
Find the equation of all common tangents.

2) f(x) = 1/x. Look at the first quadrant of the graph. P is any point on the line and the tangent line at P meets the y-axis at B and the x-axis at A. Prove that The area of triangle AOB = 2.

I'm really lost and I have no idea who to turn to.

 

[stapel]

1) A common tangent line shares the same slope. So the first step would be to set the derivatives equal to each other. Find the common slope. Then go back to the original equations, and find the points having that slope. Then find the line(s) connecting those points with that slope.

2) What is the derivative? Then, at point P = (x, 1/x), what is the tangent line? Can you find formulas for B and A?

See how far you can get with this. If you need more, please reply showing what you've got.

Thank you.

Eliz.