Question

Which of the following is true about the graph of
*f*(*x*)=8*x^*2+(2/*x)*−4?

a) *f*(*x*) is increasing on the interval
(−∞,0).

b) *f*(*x*) has a vertical asymptote at
*x*=2.

c) *f*(*x*) is concave down on the interval
(0,∞).

d) *f*(*x*) has a point of inflection at the point
(0,−4).

e) *f*(*x*) has a local minimum at the point
(0.50,2).

Suppose

*f*(*x*)=12*x**e*^(−2*x*^2)

Find any inflection points.

Answer #1

. Let f(x) = 3x^5/5 −2x^4+1. Find the following:
(a) Interval of increasing:
(b) Interval of decreasing:
(c) Local maximum(s) at x =
d) Local minimum(s) at x =
(e) Interval of concave up:
(f) Interval of concave down:
(g) Inflection point(s) at x =

(i) Given the function f(x) = x3 − 3x + 2
(a) What are the critical values of f?
(b) Find relative maximum/minimum values (if any). (c) Find
possible inflection points of f.
(d) On which intervals is f concave up or down?
(e) Sketch the graph of f.
(ii) Find a horizontal and a vertical asymptote of f(x) = 6x .
8x+3

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Given: f(x) = x^3-3x^2 -9x + 1 which (if any) of the following
statements are true?
a)f(x) has one relative max point
b) f(x) has one relative min point
c) f(x) has one inflection point
d) f(x) is increasing for all x > 0
e) f(x) is concave down at x = 2
f) f(x) crosses the vertical y axis twice
g) The graph of f '' is a parabola

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

Sketch a graph of a function having the following properties.
Make sure to label local extremes and inflection points.
1) f is increasing on (−∞, −2) and (3, 5) and decreasing on (−2,
0),(0, 3) and (5,∞).
2) f has a vertical asymptote at x = 0.
3) f approaches a value of 1 as x → ∞
4) f does not have a limit as x → −∞
5) f is concave up on (0, 4) and (8, ∞)...

Let f(x)= (x-2)/(x^2-9)
A. find the x and y-intercepts
B. find the vertical and horizontal asymptote if any
C. find f'(x) and f''(x)
D. find the critical values
E. determine the interval of increasing, decreasing, and find
any relative extreme
F. determine the interval which f(x) is concave up, concave
down, and any points of inflection

Consider the graph y=x^3+3x^2-24x+10
Determine:
a) interval(s) on which it is increasing
b) interval(s) on which it is decreasing
c) any local maxima or minima
d) interval(s) on which it is concave up
e) interval(s) on which it is concave down
f) any point(s) of inflection

f(x)= (x^2+2x-1)/x^2)
Find the
a.) x-intercept
b.) vertical and horizontal asymptote
c.) first and second derivative
d.) Is it increasing or decreasing? Identify any local
extrema
e.) Is it concave up and down? Identify any points of
reflection.

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