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Stewart_Calc_7ET ch03sec01
MULTIPLE CHOICE
1. Use the definition of the derivative to find the derivative of the function.
a.
b.
c.
d.
2. Find an equation of the tangent line to the graph of the function at the indicated point.
a.
b.
c.
d.
3. Find the derivative of the function.
a.
b.
c.
d.
4. Find the derivative of the function.
a.
b.
c.
d.
5. Find the derivative of the function.
a.
b.
c.
d.
6. Find the derivative of the function.
a.
b.
c.
d.
3
8
3
8
7. Find the derivative of the function.
a.
b.
c.
d.
8. Find the second derivative of the function.
a.
b.
c.
d.
9. Find the second derivative of the function.
a.
b.
c.
d.
10. Find an equation of the line tangent to the graph of at the point where x = 0.
a.
b.
c.
d.
11. Differentiate the function.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find in terms of .
2. Find the points on the curve where the tangent is horizontal.
3. Find the equation of the tangent to the curve at the given point.
4. Find an equation of the tangent line to the curve.
5. Find the first and the second derivatives of the function.
6. If and , find
7. Find all points at which the tangent line is horizontal on the graph of the function.
8. Find .
SHORT ANSWER
1. Let .
a. Find the derivative of f.
b. Find the point on the graph of f where the tangent line to the curve is horizontal.
c. Sketch the graph of f and the tangent line to the curve at the point found in part (b).
d. What is the rate of change of f at this point?
2. Find the derivative of the function.
3. Find the derivative of the function.
4. Find the derivative of the function.
5. Find the derivative function.
6. Find the second derivative of the function.
h(t) = (t6 + 3) sin t
7. The position function of a body moving along a coordinate line is
s(t) = 3 sin t + 2 cos t
where t is measured in seconds and s(t) in feet. Find the position, velocity, speed, and
acceleration of the body when t = .
