In the function:  f(x)= (4x^2)/((x^2)+4)  What are the critical numbers of the function?  Where is the function increasing and decreasing in interval notation?  What are the x-coordinates of all local minima and local maxima?

Question

In the function: 

f(x)= (4x^2)/((x^2)+4) 

What are the critical numbers of the function? 

Where is the function increasing and decreasing in interval notation? 

What are the x-coordinates of all local minima and local maxima? 

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: A painting attributed to Vermeer (1632–1675), which should contain no more than 96.2% of its origina...

A: To determine the time (in years) of forgery, A painting attributed to Vermeer (1632-1675), which sho...

Q: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question ...

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential equat...

A: Click to see the answer

Q: (sin t)y′+(cos t)y=et,y(1)=a,0<t<π

A: Given,The initial value problem(sin t)y′+(cos t)y=et, y(1)=a,0<t<πConsider,

Q: How can you sometimes evaluate indefinite integrals by substitution? Give examples.

A: "Integration by Substitution" (also called "u-Substitution" or "The Reverse Chain Rule") is a method...

Q: Find the area enclosed by the ellipse x2/ a2 + y2 /b2 = 1

A: Given,

Q: Write an integral for the area of the surface generated by revolv-ing the curve y = cos x, -pai/2&lt...

A: The given curve is

Q: PROBLEM 4 (cos² x sin x-sin x cos x+sin³ x' lim Evaluate analytically the х2

A: Click to see the answer

Q: Consider a region bounded by the graphs of y = x4 and y = x5. Show that the center of mass lies outs...

A: It is given that the density of the plate is  and the region bounded by the graphs of y = x4 and y =...

Q: The marginal cost of printing a poster when x posters have been printed is dc/ dx =1/(2(sqrt(x)) dol...

A: It is given that, the marginal cost of printing a poster when (x) posters have been printed is

Q: How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(x) ove...

A: Given:How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(...

Q: What is the age of a sample of charcoal in which 90% of the carbon-14 originally present has decayed...

A: Consider half-life for charcoal sample.

Q: The charcoal from a tree killed in the volcanic eruption that formed Crater Lake in Oregon contained...

A: The half-life of carbon-14 is 5700 years. The decay constant, k is defined to be

Q: Find the area of the propeller-shaped region enclosed by the      curves      x - y^(1/3) = 0 and x ...

A: First we have to find where the curves intersect. Set x equal for those curves and solve for y.

Q: Find the domain of f(g(x))

A: Given that two functions: Find the domain of (fog)(x) 

Q: A particle of mass m starts from rest at time t = 0 and is moved along the x-axis with constant acce...

A: Given information:

Q: Suppose f(r)=1+3r^2. Evaluate the function for each of the following values of its argument: 1. with...

A: Find the function by substituting the given arguments.

Q: Find the area of the shaded region. У 3 x = y - 2 y = 1 x = ey -3 -1 y = -1 -3 3. 2. 2. 2.

A: To find the area of the shaded region which is bounded by the below functions.

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y = 0...

A: Given,

Q: y′+2y=te−2t,y(1)=0

A: Click to see the answer

Q: What are the six basic hyperbolic functions? Comment on their domains, ranges, and graphs. What are ...

A: The six basic hyperbolic functions are sinh(x) , cosh(x) , tanh(x) ,csch(x) , sech(x) ,coth(x) 

Q: 1 Find the area of the region (see figure) in two ways. a. By integrating with respect to y. b. Usin...

A: Find area of the shaded region in two waysUsing integrationUsing Geometry

Q: Find the volume of the solid formed by revolving the re-gion bounded by the graphs of y = sin x + se...

A: The given graph of the functions are

Q: Find the length of the curve y = x2, 0 <=x <=sqrt(3)/2.

A: Given information:

Q: Find the centroid of a thin, flat plate covering the region enclosed by the x-axis, the lines x = 2 ...

A: Given information:

Q: Find the areas of the regions enclosed by the curves in Exercises 83–86. 83. 4x2 + y = 4 and x4 - y ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find the areas of the regions enclosed by the lines and curves in Exercises 87–94. 87. y = 2 sin x a...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Graph y = log a 2 as a function of a over the interval 0<a<= 4.

A: Given that 0<a≤4 Rewrite the function as: 

Q: Find the difference quotient g(x)=1/x^2   (g(x)-g(6))/x-6   x cannot =6

A: Plug x=6 in g(x) and find g(6)

Q: Suppose that a certain population satisfies the initial value problem dy/dt=r(t)y−k,y(0)=y0,dy/dt=r...

A: Calculation:

Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The regi...

A: Given information:

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x and y = x...

A: Given information:

Q: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh...

A: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh...

Q: find the volume . The base of the solid is the region bounded by the parabola y2 = 4x and the line x...

A: The base of the solid bounded by the parabola y^2=4x and the line x=1. And each cross section perpen...

Q: Evaluate (if possible) the sine, cosine, and tangent of the real number t. (If an answer is undefine...

A: Given,

Q: Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

A: The given two curves are,

Q: a. Find the center of mass of a thin plate of constant density cov-ering the region between the curv...

A: (a)Given information:

Q: 6.4.41 Question Help Let R be the region bounded by y =x², x= 1, and y= 0. Use the shell method to f...

A: Click to see the answer

Q: Find the volume of the solid generated by revolving the region enclosed by the graphs of y = ex>2...

A: Click to see the answer

Q: The frozen remains of a young Incan woman were discovered by archeologist Johan Reinhard on Mt. Ampa...

A: Given,The Body of the woman is found in year 1995.

Q: For the given functions f and g, find the following. For parts (a-d), also find the domain. f(x)=squ...

A: Solve (f+g)(x) and find its domain.

Q: A right-circular conical tank, point down, with top radius 5 ft and height 10 ft is filled with a li...

A: Given A right-circular conical tank, point down, with top radius 5 ft and height 10 ft is filled wit...

Q: Consider the function. |r + 7|– |r – 7| f(x) = Estimate the following by evaluating fat x-values nea...

A: Given,

Q: The viewing portion of the rectangular glass window in a typical fish tank at the New England Aquari...

A: Consider the given statement of the question,Since, the force on the window is proportional to the d...

Q: Find the center of mass of a thin, flat plate covering the region enclosed by the parabola y2 = x an...

A: To determine the centre of mass of the plate.

Q: Consider the following two equations. yA f. 1 < g(x). Find the values of x for which f(x)

A: We are given two functions f and g in the question.We need to find the values of x for which f(x) &l...

Q: A bead is formed from a sphere of radius 5 by drilling through a diameter of the sphere with a drill...

A: Given:A bead is formed from a sphere of radius 5 by drilling through a diameter of the sphere with a...

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1 ...

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has bot...

Q: Suppose that a certain population satisfies the initial value problem dy/dt=r(t)y−k,y(0)=y0,dy/dt=r...

A: Given:

Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded by the ...

A: Recall the fact.