Stewart_Calc_7ET ch02sec07
MULTIPLE CHOICE
1. If an equation of the tangent line to the curve at the point where
a.
b.
c.
d.
e.
None of these
2. Use the definition of the derivative to find
a.
b.
c.
d.
e.
does not exist
3. The cost (in dollars) of producing x units of a certain commodity is
Find the instantaneous rate of change with respect to x when (This is called the
marginal cost.)
a.
b.
c.
d.
e.
4. If the tangent line to passes through the point
a.
b.
c.
d.
e.
5. Find an equation of the tangent line to the curve at the point .
a.
b.
c.
d.
e.
None of these
6. Find an equation of the tangent line to the parabola at the point .
a.
b.
c.
d.
e.
7. The slope of the tangent line to the graph of the exponential function at the point is
Estimate the slope to three decimal places.
a.
b.
c.
d.
e.
f.
8. Find the slope of the tangent line to the curve at the point .
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the derivative of the function.
2. If a cylindrical tank holds gallons of water, which can be drained from the bottom of
the tank in an hour, then Torricelli’s Law gives the volume of water remaining in the tank
after t minutes as
Find the rate at which the water is flowing out of the tank (the instantaneous rate of change
of V with respect to t) as a function of t.
3. The cost (in dollars) of producing x units of a certain commodity is
Find the average rate of change with respect to x when the production level is changed from
