1. Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward.
A. (negative infinity, infinity)
B. (negative infinity, -1) U (1, infinity)
C. (negative infinity, 0) U (0, infinity)
D. (1, infinity)
E. none of these
I got C. I found the second derivative and used the interval test.

2. If f(3)=0, f’(3)=6, g(3)=1, g’(3)=1/3, find h’(3) if h(x)=[f(x)] / [g(x)]
A. 18
B. 6
C. -6
D. -2
E. none of these
I got B. I figured out h'(x) in terms of f(x), g(x), f'(x), and g'(x) and plugged in the given numbers.

3. Find all open intervals on which f(x)=x/(x^2+x-2) is decreasing.
A. (negative infinity, infinity)
B. (negative infinity, 0)
C. (negative infinity, -2) U (1, infinity)
D. (negative infinity, -2) U (-2,1) U (1, infinity)
E. none of these
I got C. I found the first derivative and critical numbers. Then I used the interval test.

Thank you for checking my answers.

1. 👍 0
2. 👎 0
3. 👁 657
1. #1 ok

#2
h' = (f'g-fg')/g^2 = (6*1-0*1/3)/1 = 6
So, B is correct

#3
f' = -(x^2+2)/(x^2+x-2)^2
f' < 0 for all x
So, (D) is correct

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Calculus

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical

2. ### Calculus

Sketch the graph of the function that has the following properties. f is continuous on (-infinity, infinity). points: (-1,2), (0, 0), (-1,0) f'(x)>0 at (-infinity, -1) f'(-1)=0 f'(x)0 on (1, infinity) f"(x)0 on (0, infinity) I'm

3. ### Math

Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x? a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity b. f(x) approaches negative

4. ### cal

Find the largest open intervals where the function is concave upward. f(x)=x^4-8x^2

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For

2. ### calculus

If f(x) = 3 cos^2(x) − 6 sin(x) 0 ≤ x ≤ 2π Find the intervals of increase and decrease, the intervals of concave up and concave down, local maximum values, local minimum values, and inflection point

3. ### Calculus

Suppose you know that f(x) is an odd functon on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5. List ALL intervals on which the

4. ### help math

a partial moves along the x-axis so that its velocity at time t, for 0< = t = < 6, is given by a differentiable function v whose graph is shown above. The velocity is 0 at t=0, t=5, and the graph has horizontal tangents at t=4.

1. ### Please check my Calculus

1. Given f(x)=-6/x, choose the correct statement A. The graph of f is concave upward on the interval (negative infinity, 0) B. The graph of f is concave downward on the interval (negative infinity, 0) C. The graph of f is concave

2. ### Calculus

1. The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = –3. Which of the following statements must be true? A. The graph of f is always concave down. B. The graph of f has an inflection point at x =

3. ### Calc

Let F be the function defined by F(X)=12X to the 2/3 power minus 4X Find the intervals of which F is increasing? Find X & Y coordinates of all relative max. pts? Find X and Y Coordinates of all relative min pts? Find the intervals

4. ### calculus

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical