Answered: h(x) = 4/((x-1)^2) Show from the…

h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 84E

See similar textbooks

Related questions

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

Q: Find the derivative by the limit process. f(x) = 7 − x2

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

Q: ation. -5 -5

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule]

Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: tion 1. Find the rule of the piecewise function

A: 1. From the graph given , the piecewise distribution of the function is as follows , fx=x+1 ,…

Q: Use second derivative test, If x3 f(x) = 25x + 5 then f(x) has a 3 local maximum at the point x = -3…

Q: Find the derivative of the transcendental function. h(x) = - 14 sec x X h'(x) = -5x2-14 secx-tanx

A: We need to find the derivative of the given transcendental function. hx=5x-14secx

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2 As we know that; To calculate the critical point, f'x=0.

Q: Find the derivative of the function by the limit process. f(x) = 6/x^2

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: True or False The cube root function is odd and is decreasing on the interval (-∞,∞).

A: we have to tell whether the given statement is True or False

Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

Q: Use derivative to identify open intervals on which the function is increasing or decreasing.…

Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

Q: f(x) = ln (1/x^6)

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given, The function is fx=7x-9.

Q: 2. Find the derivative of f(x) = -4x2 + 3x + 2 from first principles (i.e. the limit definition of a…

Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

Q: Find the value of the derivative of the function at the given point. f(x) = 2x2 - 3x; (- 1,5)…

A: The function is given by fx = 2x2-3x To evaluate : The value of the derivative of the function at…

Q: equation of the function f whose graph passes thro f'(x) = x/25 - x²

Q: 5. ƒ(x) = (x²+x−3)√√x²+x=3

Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x) To find:- Use limit Definition of a derivative to find f'(3)

Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: Sketch the graph of an increasing function such that f'' (x) changes from + to − at x = 2 and from −…

A: Sketch the graph of an increasing function such that f”(x) changes from + to - at x = 2 as follows.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: prove that f(x)=3x^3-4x^2-x-3 is continuous over [-3,3]

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below

Q: IT Uonsəni (a) Use the Second Derivative Test to find the local extreme values of the function f(x)…

Q: Find the derivative of f(x) = arctan x In(6x² + 6x – 4) 1 1 arctan x 6x2+6x-4

A: Here the given function fx=tan-1x ln6x2+6x-4

Question

h(x) = 4/((x-1)^2)

Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

How can you determine whether a function is odd or even from the formula of the function?
What is the purpose of the Intermediate Value Theorem?
Determine dimension x to 3 decimal places.
Find the local maximum and minimum values of f(x) = x^5 -5x +3 using the second derivative test when it is not possible use the first derivative test
Isn't the ln function supposed to have absolute brackets? like ln|y-1| instead of ln(y-1)?
Two functions are said to have the same end behaviorif their ratio approaches 1 as x -> + infinity and x-> - infinity. Show that 3x 5 - 5x3 + 2x and 3x5 have the same end behavior.
How do you find the derivative of f(x) = 5 using the limit definition of derivatives? I know it is 0, but how do I show the work?
Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum using the second derivative test.
True or False The cube root function is odd and is decreasing on the interval (-∞,∞).
prove that f(x)=3x^3-4x^2-x-3 is continuous over [-3,3] give an example of a function f whose third derivative exist at x=o but whose fourth derivative does not.
The base of a rectangular box, open at the top, is to be three times as long as it is wide.Find the dimensions of the box with minimal surface area if the volume of the box is to be 2250 cubicinches. Show and organize your work; use the first derivative test or the second derivative test orother tools to check that yours is the desired optimal solution.
lim h--->0 (f(2+h)-f(2)) / h , where f(x)=4x+8