AP CALCULUS BC - CHAPTER 3 TEST - OPEN ENDED SECTION
Name: ________________________________
1.
PERIOD 3
CALCULATORS OK - IF ROUNDING 3 decimal places
2.
The figure to the right shows the graph of the
derivative of a continuous function f(x) on [-4, 4].
a.
State in interval notation for what values
of x is f(x) increasing. JUSTIFY.
b.
State in interval notation for what values
of x is f(x) decreasing. JUSTIFY.
c.
State the x-coordinate of ALL points of relative
extrema. Classify them as rel. max. or rel. min.
JUSTIFY.
d.
Identify ALL POI. State in interval notation
where f(x) is concave up or concave down.
e.
If f(0) = 1, sketch a possible graph for f(x) on [0, 4].
3.
Let f(x) be a twice-differentiable function (both f(x) and f'(x) are differentiable functions) for all real numbers.
f(2)=5 and f(5)=2. Lets define g(x) as g(x)=f(f(x)).
a.
b.
JUSTIFY why there must be a value c on (2, 5) such that f'(c)=-1.
SHOW that g'(2)=g'(5). Use this result to JUSTIFY that there must be a value k on (2, 5) such that g''(k)=0.
4.
f ( x)  2 x 3  4 x  1 at x=½.
a.
Find the linearization of
b.
Use the previous linearization to estimate the value of f (0.501) .
c.
d.
What will be the error of the above estimation.
Determine df when x=½ and dx  0.001
AP CALCULUS BC - CHAPTER 3 TEST - OPEN ENDED SECTION
Name: __________________________________
1.
PERIOD 5/6
CALCULATORS OK - IF ROUNDING 3 decimal places
A manufacturer needs to make a cylindrical can that hold 1.5 liters of liquid. Determine the dimensions of the
can that will minimize the amount of material used in its construction. ( 1 liter = 1000 cubic centimeters)
2.
The figure to the right shows the graph of the
derivative of a continuous function f(x) on [-5, 5].
a.
State in interval notation for what values
of x is f(x) increasing. JUSTIFY.
b.
State in interval notation for what values
of x is f(x) decreasing. JUSTIFY.
c.
State the x-coordinate of ALL points of relative
extrema. Classify them as rel. max. or rel. min.
JUSTIFY.
d.
Identify ALL POI. State in interval notation
where f(x) is concave up or concave down.
e.
If f(0) = 1, sketch a possible graph for f(x) on [0, 5].
3.
4.
f ( x)   x 3  4 x 2  1 at x=½.
a.
Find the linearization of
b.
Use the previous linearization to estimate the value of f (0.501) .
c.
d.
What will be the error of the above estimation.
Determine df when x=½ and dx  0.001
AP CALCULUS BC - CHAPTER 3 TEST - OPEN ENDED SECTION
Name: _________________________________
1.
PERIOD 10/11
CALCULATORS OK - IF ROUNDING 3 decimal places
A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km
downstream on the opposite bank, as quickly as possible. He could proceed in any of three ways:
1.
Row his boat directly across the river to point C and then run to B.
2.
Row directly to point B.
3.
Row to some point D between C and B and then run to point B.
If he can row at 6 km/h and run at 8 km/h, where should he land to reach point B as soon as possible?
2.
The figure to the right shows the graph of the
derivative of a continuous function f(x) on [-3, 4].
a.
State in interval notation for what values
of x is f(x) increasing. JUSTIFY.
b.
State in interval notation for what values
of x is f(x) decreasing. JUSTIFY.
c.
State the x-coordinate of ALL points of relative
extrema. Classify them as rel. max. or rel. min.
JUSTIFY.
d.
Identify ALL POI. State in interval notation
where f(x) is concave up or concave down.
e.
If f(0) = 1, sketch a possible graph for f(x) on [0, 4].
4.
f ( x)  10 x 2  15 x  1 at x=-½.
a.
Find the linearization of
b.
Use the previous linearization to estimate the value of f (0.501) .
c.
d.
What will be the error of the above estimation.
Determine df when x=½ and dx  0.001