This document contains math homework/study work problems involving tangent and normal lines to curves, derivatives of functions, and applications of the product rule. There are 7 problems finding equations of tangent or normal lines to curves at given points, plotting the curves and lines. One problem involves proving an identity about the derivative of a composite function using the product rule twice.

1. Math HW/SW
24. ( ) ( )( )
30*. ( )
32. ( )
36. * ( )+
43*. The tangent line to the curve at the point (2, 4)
44*. The tangent line to the curve at the point (2, 1)
47. Find an equation of the line tangent to the curve and parallel to the line
. Support your answer by plotting the curve and the two lines in the same window.
49. Find an equation of each of the normal lines to the curve that is parallel to the line
. Support your answers by plotting the curve and the lines in the same window.
51. Find an equation of each of the lines through the point (4, 13) that is tangent to the curve
. Support your answers by plotting the curve and the lines in the same window.
53. If f, g, and h are functions and ( ) ( ) ( ) ( ), prove that if ( ) ( ) ( ) exist,
( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Hint: Apply the product rule twice
*Support your answer by plotting the curve and the lines in the same window.