For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
1)For the function f(x)=6x^2−2x, evaluate and simplify.
f(x+h)−f(x)/h
2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6
3)A bacteria culture starts with 820820 bacteria and grows at a
rate proportional to its size. After 22 hours there will be
16401640 bacteria.
(a) Express the population PP after tt hours as a function of tt.
Be sure to keep at least 4 significant figures on the growth
rate.
P(t)P(t)=
(b) What will be the population after 8 hours?
bacteria
(c) How long will it...
On what interval(s) is the function
f\left(x\right)=2x-\ln\left(3x^2\right)f(x)=2x−ln(3x 2 ) both
decreasing and concave up?
You will only earn credit by showing your work algebraically
(applying Calculus).
1. Find the critical numbers for the following functions
(a) f(x) = 2x 3 − 6x
(b) f(x) = − cos(x) − 1 2 x, [0, 2π]
2. Use the first derivative test to determine any relative
extrema for the given function
f(x) = 2x 3 − 24x + 7
Find the real zeros of the function f(x) = -(x+1)^3(x-2)^2 and
their corresponding multiplicities. Use the information along with
a sign chart (diagram) and then the end behavior to provide a rough
sketch of the graph of the polynomial.
Find a power series for the function, centered at
c.
f(x) =
3
2x − 1
, c = 2
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)