Math 1100 Section 4 Test2
Name:
Read all directions carefully and show all your work for full credit. Pay close
attention to how much each problem and each part of each problem is worth.
Good Luck!!!
1.
2.
3.
4.
5.
6.
(10pts)
(10pts)
(30pts)
(10pts)
(15pts)
(30pts)
total
p
1. (10 points) If g(x) = 5 5x + 7 then nd g00( 56 )
2. (10 points) Find the equation of the tangent line to the curve y2x x2 + y2 = 4
at the point (0; 2)
2(x2 4)
3. Sketch the graph of the following function f (x) = x2 1 using the following strategy.
(a) (5 points) Find all x and y intercepts of the function
(b) (5 points) Find all horizontal and vertical asymptotes
(c) (5 points) Determine the intervals on which the function is increasing and
decreasing.
(d) (3 points) State where all minimum's and maximum's occur. If there are
none state why.
(e) (5 points) Determine the intervals on which the function is concave up and
concave down.
(f) (2 points) Find all inection points. If there are none state why.
(g) (5 points) Sketch the graph of the function using the above information.
4. (10 points) Use the second derivative test to clasify all relative extrema of the
function H (x) = 41 x4 + 13 x3 + 6x2 + 10
5. (15 points) Farmer John is building four new rectangular pig pens. He has
decided to construct the pens by dividing one big pen into four pens of equal
size. See picture below or on board. If Farmer John has a total of 300ft of
fence, what is the maximum area that he can enclose?
6. (5 points each) Find the derivative of the following functions.
(a) A(x) = ln(6x)
(b)
B (x) = e19x
(c) C (x) = log4(x2 + 1)
(d)
(e)
D(x) = 32x4
E (x) = ln
x3 +x
q x2+1
x 2
4x5+2x
100
)
(f) F (x) = log10(
10005x2