Millersville University Name
Department of Mathematics
MATH 161, Quiz 6
February 27, 2004
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit.
1. Find the equation of the tangent line to the curve x3y3= 9yat the point with coordi-
nates (1,3). You may use implicit differentiation.
Applying implicit differentiation produces:
d
dx hx3y3i=d
dx [9y]
3x2y3+x3d
dx hy3i= 9y0(x)
3x2y3+x33y2y0(x) = 9y0(x)
3x2y3=−3x3y2y0(x) + 9y0(x)
3x2y3=−3x3y2+ 9y0(x)
x2y3=−x3y2+ 3y0(x)
x2y3
3−x3y2=y0(x)
Thus the slope of the tangent line at the point with coordinates (x, y) = (1,3) is
m=y0(1) = 1233
3−1332=27
3−9=27
−6=−9
2.
Using the point-slope formula for a line we get as the equation of the tangent line:
m=y−y1
x−x1
−9
2=y−3
x−1
−9
2(x−1) = y−3
−9
2x+9
2=y−3
−9
2x+9
2+ 3 = y
−9
2x+15
2=y
