Math 1100 Section 4 Review 2 (2.6-4.5) Due: Day of Test 2
This will be graded on completion so try all of the problems. For these types of
problems it is often necessary to simplify answers to nd all critical values!!
p
1. If f (x) = 3 9x + 7 then nd f 000( 32 )
2. Find the equation of the tangent line to the curve x2y +5x 6y = 5
at the point (1; 0).
3. Sketch the graph of the function f (x) = x3 + x2 6x + x2 + x 6
using the following strategy.
(a) Find all x and y intercepts (Hint: try grouping)
(b) Find all horizontal and vertical asymptotes.
(c) Find where the function is increasing and decreasing.
(d) Find any relative minimum's and maximum's.
(e) Determine the intervals on which the function is concave up
and concave down
(f) Find all inection points
(g) Sketch the graph with all of the above information.
4. Sketch the graph of the function f (x) =
strategy.
2
x2
x
+5
1
using the following
(a) Find all x and y intercepts
(b) Find all horizontal and vertical asymptotes.
(c) Find where the function is increasing and decreasing.
(d) Find any relative minimum's and maximum's.
(e) Determine the intervals on which the function is concave up
and concave down
(f) Find all inection points
(g) Sketch the graph with all of the above information.
5. Sketch the graph of the function f (x) = 3 22+15
+1 using the following
strategy.
x
x
(a) Find all x and y intercepts
(b) Find all horizontal and vertical asymptotes.
(c) Find where the function is increasing and decreasing.
(d) Find any relative minimum's and maximum's.
(e) Determine the intervals on which the function is concave up
and concave down
(f) Find all inection points
(g) Sketch the graph with all of the above information.
6. Use the second derivative test to classify all relative extrema of
the function G(x) = x5 60x3 + 1125x + 1600
7. A norman window is formed by attaching a semicircle to the top of
an ordinary rectangular window. Find the dimensions of a Norman
window of maximum area if the total perimeter is 16 + 2 feet.
(Hint see Chapter 3 number 17 for a picture)
8. Find the derivatives of the following functions.
(a) ln(4x)
(b) e14
q 2+1
(c) ln 3 2 +7
(d) e5 5 6 3+2
(e) 43 2+
(f) log6(5 4 714 +5)
x
x
x
x
x
x
lnx
x
x