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Graded Midterm Exam 1  
What is the
limit of the function in the graph at x = 4?
  What is the
slope of the secant line of the function y = -2x2 + 3x – 1 between x
= 2 and x = 6?
What is the derivative of
the function f(x) = esin
  
and it takes her 20
minutes to get to school, what is her average rate of speed in miles per hour?
The answer is 6 mph.
Find the
slope of the line tangent to f(x) = x2 – x at
the point x = 2.
Suppose f(x)
= x0, what is f’(x)
For which
values of k will the line y = x + k meet the parabola of the equation y = −x2
+ 4x − 8
in two distinct points? 
Compute the derivative of
the function f (x) = (−x + 3x2 – x-2)
(3x − x)
 
What is the limit of the
function in the graph at x = 4?
What is the derivative of y
= xex + x2?
Find all
of the critical points of p(t). p(t)
= t2 + 5t + 6.
A rectangular prism has
dimensions 3 inches by 12 inches by 4 inches. What is the volume of the prism?
Which
equation is represented by the following graph?
 
An airplane flies at an altitude of 5 miles
toward a point directly over an observer.
The speed of the plane is 600 miles per hour.
Find the rate at which the angle of elevation
is changing when the angle is π /6.
If the graph
of the derivative of f(x) is shown, at which x-coordinates would f(x) have a
point of inflection?
A man 6 feet tall walks at
a rate of 5 ft /sec away from a light that is 15 feet above the ground.
When he is 10 feet from
the base of the light, at what rate is the tip of his shadow moving?
A particle moves along the
x-axis, with its position x given by x(t) = t − cos
t.
At which of the following
times is the velocity of the particle equal to 0?
What is the slope of the
line tangent to the curve x2 y2 = 1 at the point (1, 1)?
Express distance in terms
of rate and time.
Evaluate the
following as true or false.
What is the
slope of the secant line of the function y = −2x2 + 3x − 1 between x
= x1 and x = x2?
A right circular cylinder
has a diameter of 12 in. and a height of 12 in.
If water is flowing in at the rate of 4π in per minute, find the rate of change of the height when the height is
4 in.
What is the slope of the
line tangent to the curve x3 + y3 = 2x2 y2
at the point (1,1)?
Evaluate the following as
true or false.
Compute the derivative of
the function:
 
An open box with a square
base is to have a volume of 4000 in3. Find the length of the side of
the square base
that would result in the
least amount of material needed to construct the box.
True or false?
The tangent line to the
highest point of an open downward parabola
(or lowest point of an
open upward parabola) has slope m = 0.
If dy
/dx is undefined for a given value of x, then the line tangent to
the curve y = f(x) at that value does not exist.
What is the derivative of y
= x ln x − x?
The position of a car at
time t is given by the function p (t) = t2 − 3t − 26.
At what time will the
velocity of the car be 11? Assume t ≥ 0.
What is the average rate
of change of the function y = 2x2 + 3 between x
= 2 and x = 4?
Compute the derivative of
the function
 What is the derivative of the function f(x) =   The graph of the
derivative of f(x) is shown in the figure. Which
of the following could be the graph of f(x)?
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