Calculus, Unit 5: TestA_teacher, page 1
1. Differentiate implicitly to find y’ where xy2 = x sin(x).
2. Differentiate implicitly to find y’ where cos(x)sin(y) = x3.
3. Differentiate implicitly to find the x-position(s) at which the normal line(s) to
the curve given by xy2 = 1 are horizontal.
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Calculus, Unit 5: TestA_teacher, page 2
4. Differentiate implicitly to find y’’ in terms of x and y where x–1 + y1/2 = 3.
5. Consider a circle having a radius of 3 and center at (2, 4). Locate the point(s)
at which the tangent line(s) to this circle have a slope equal to the slope of the
line connecting the origin and the center of the circle. (Differentiate implicitly.)
6. Find Q’ where Q(x) =cos( tan(x) )
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Calculus, Unit 5: TestA_teacher, page 3
7. An object is moving left-to-right along the curve y = (4/3)x3. At what point(s)
on the curve is the x component of its velocity equal to twice the y component?
8. A spherical snowball 10 cm in diameter is melting at the rate of 3 cm3/min yet
still maintains its spherical shape. What is the rate of change of its radius when
the radius is 2?
9. What is g’(x) evaluated at x = 2 radians where g is a function of x such that
g2x2 + 3sin(x) = 6? (Assume that g(2) = –1.)
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Calculus, Unit 5: TestA_teacher, page 4
10. Assuming that y is a function of x, find y’ in terms of x and y where
1/(x + y2) = y1/2.
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