I think I figured out the first two questions, but I have three more puzzlers to go. Can anyone help?
3. Verify that the line 4x-y+11+0 is tangent to the curve y=(16/x²)-1. Then determine the point of tangency.
I started this question off by finding the derivative of the curve, and I got y'= -32x(-3), where -3 is the exponent on x. I also isolated for y in the line and I got y=4x+11.
I have no idea where to go from here.
4. For what values of "a" and "b" will the parabola y=x²+ax+b be tangent to the curve y=x²√x+1 at the point (3, 18)?
*Stares blankly at the question.*
5. Find the AREA of the triangle formed by the three points on the curve y=[x²-1 / x²+1]² where the tangent lines are horizontal.
We haven't done anything like this before! We never even learned the equations on how to do this! All we have discussed in this course (which started a couple weeks ago) has been limits, derivatives, power rule, etc.