1. (6 points) Find
dt
dx for 3 x = −2z − t
2. (10 points) Find
dx
dy for 3 5 2 5 2 2
x + xy = y +
3. (8 points) Find the differential dy for
x
y x
1 4 2 = +
4. Use the equation 3 4 5 2
y = x − x − to answer the following questions.
a) (10 points) Write the equation of the tangent line drawn to this curve at x = 2 . Answer in
general form.
b) (2 points) Find the slope of the normal line drawn to this curve at x = 2 .
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5. Use the equation 3 2
y = −x + 6x to answer the following questions.
a) (2 points) Find the domain of y.
b) (4 points) Find the x-intercept(s) as points.
c) (2 points) Find the y-intercept(s) as points.
d) (10 points) Find any maximum and minimum points.
e) (6 points) Find any points of inflection.
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f) (8 points) Sketch the function.
6. (6 points) Is the curve 3 2 2 1 4 3 y = x + x + x − increasing or decreasing at x = −2 ? Show your work
to justify your answer.
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7. (6 points) Is the curve 2 5 4 4 3 y = x + x + concave upward or concave downward at x = −2 ?
Explain your answer.
8. Use the curve
1
4 8
+
− = x
x
y to answer the following questions.
a) (2 points) Find the domain of y.
b) (2 points) Find the vertical asymptotes for the curve.
c) (4 points) Find the horizontal asymptotes for the curve. (No limits, no credit)
d) (4 points) Find x- and y-intercepts as points.
9. (8 points) Find the second derivative for y = 4x +1