10.7#11

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I do not understand how to solve this problem. I tried taking the
derivative of each x,y, and z and then solving for t.

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Hmmm, you might be trying to represent the tangent line p using the symmetric equations. You could make that work but the parametric form r(t)=u+tv is better for this. And solving for t that way won't work because you are confusing the t that would be the parameter in the parametric equations for the line--that you solve for to get the symmetric equations--for the t that's a variable in the curve. THOSE ARE PARAMETERS FOR DIFFERENT CURVES. You can get the t for the curve from knowing that the point (7, 9, 32) is on the curve, like for example from the equation t^3-1=7 (hence t=2). From the definition of tangent line on the top of page 585 (in my book anyway) you know it has to pass through the point (7,9,32) and be parallel to r'(2)=<12,12,80>,