Math 1100 Section 4 Final Review (1.4-7.4) Due: Day of Final
This will be graded on completion so try all of the problems.
x2 15x
1. Find limx!3 xx3 +2
2 +4x 21
2. If T (x) = x12 4x3 + 5 then nd the equation of the tangent line
at the point ( 1; 5)
3. If F (x) = x3ln(x) then nd F 0(x).
0
4. If G(x) = e2xx2+5
7x then nd G (x).
p
5. If H (x) = 7 5x2 10x + 7 then nd H 0(x).
6. Use the limit denition of the derivative to nd f 0(x) where f (x) =
3x2 + 5x 9.
p
p
7. If R(x) = 3 3x2 5 then nd R00( 2)
8. Find the equation of the tangent line to the curve y3x x2 + y2 = 4
at the point (0,2).
9. Sketch the graph of the function P (x) = x3 3x2 + 9x using the
following strategy.
(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
10. Tito (a hippie) would like to build a fence in the shape of two
giant peace symbols that touch at a point in which to keep all of
his pigs. If Tito has 40 + 80 feet of fence what is the maximum
area that he can enclose?
11. If Y (x) = 13x2 3x+6 then nd Y 0(x).
12. If W (x) = log7(3x5 9x4) then nd W 0(x).
p
R
13. Find 6x3 5 x7 x4 + 5exdx
p
R
14. Find 12x3 9 x4 + 6dx
R
15. Find (x2 3x)lnxdx.
16. Find the area bounded by the curves y = 3x2 + 5x + 6 and y =
x3 + x + 6
R
17. Find 11 x110 dx
18. If U (x; y; z; w) = x2ey2z ln(wxyz ) + w2 then nd Ux, Uy , Uz , and
Uw and evaluate each at the point (2,1,3,4)