BC 1
Quiz #5
Show all appropriate work clearly for full credit.
1.
Name:_________________
NO CALCULATORS
For each function below, find its first derivative. Do not simplify the result.
a.
F  x   3 x 2  e3x
 
b.   x   e x  sin x5
3
(x) =
c.
x


g  x   2

 2 x  5x 
5
g(x) =
d.


h  x   5 x 2  3x  2 x
h(x) =
BC 1
2.
Quiz #5
Name:_________________
Suppose q  x     g  x   . If (1) = –3, (1) = 4, (2) = –2, (2) = 1, g(1) = 2, g(1) = –4,
g(2) = 1, and g(2) = –3, what is the value of q(2)?
f ( x)
, and L( x)  f  g ( x)  where the graphs of f and g are
g ( x)
shown below. Estimate the quantities in a.- c. . Be sure there is enough work or explanation so that I can
recreate your results.
3. Suppose that h( x)  f ( x)  g ( x), k ( x) 
y  f ( x)
a. h(1)
b. k (1.8)
c. L(1)
y  g ( x)
BC 1
4.
Quiz #5
Name:_________________
Suppose  is the function shown at
the right.
Graph of f
12
Note that the graph of f has:
A zero at x  3.4;
Local maxs and mins at
x  2, x  1, x  5.
8
4
2
1
1
2
3
4
5
4
8
a.


Is g  x   2 x  f x 2  3 increasing or decreasing at x  1 ? Justify your answer clearly and
completely.
b.


Continuing with the same graph of y  f  x  from above, if g  x   2 x  f x 2  3 , is g  x 
concave up or concave down at x = 1? Justify your answer clearly and completely.
BC 1
Quiz #5
Name:_________________
5. Consider the tangent line to the graph of f ( x)  x3  6 x 2  10 x  4 at a point x = a. Find all values of
a such that the y-intercept of the tangent line will be negative. The graph of f is shown below.