3. What is a rational function? What does it mean for arational function to be proper? Improper?

Q: Find the intervals on which ƒ is increasing and the intervals on which it is decreasing.

A:

Q: Any rational function is continuous wherever it is defined; that is, it is continuous on its…

A: We know thatPoint No.1: the composition of continuous functions is continuous.Point No.2:…

Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

Q: Find the absolute extrema of f(x)=x/(9-x) on the interval[5,9]

A: fx=x9-x  ,  5, 9 Differentiating with respect to x, we get f/x=dxdx·9-x+d9-xdx·x…

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing.…

A: The solution for the above answer is as shown below..

Q: 15. Find the interval on which f(x) = x³ – 3x² – 144x – 140 is concave up and the interval on which…

A: Point of inflection is a  point where 2nd derivative of a function is 0.

Q: What is the value of c in the interval (9, 64) guaranteed by the Mean Value Theorem for the function…

A:

Q: What are the zeros of f(x)=2cos(3x)+1 on the interval [0,π]?

A: We have the given function as fx=2cos3x+1. In order to find the zeros of the function fx, we must…

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A:

Q: 6. True or False The cube function is odd and is increasing on the interval (-o, ).

A: True We know that, A function f is said to be odd if f(-x)=-f(x) We have a cube function that is…

Q: Given the function f (x) = 3x25 – 6x24. Determine the intervals for which the function - is…

A:

Q: Find the linerization  of f(x)=x^3  near x=1 . use that linerization to approximate (1.1)^3

A: Linearization of f(x) near x=a is given by f(x)=f(a)+f'(a)[x-a] Where f'(x) is first derivative of…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given: f(x)=x29-x2 To Find: Intervals of increasing and decreasing on (-3,3). Concept: (a). if…

Q: Find and classify the extreme values of f(x)=6x^4 - 4x^6 over the interval [-2,2]

A:

Q: Write cosh(In(x)) as a rational function of x.

A: write coshlnx as a rational function of x

Q: 1. X > VX + 4 3+x 2. > 8 x+1 3. 4X 2 2 X+2

A: Since you have asked multiple questions, we will solve the first three questions for you. If you…

Q: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: 10. ( ) Find the absolute extrema of the funcion f(x) = 3 Vx2 - x on the interval -1, 1.

A:

Q: 2. Will the limit of all polynomial functions / (x) as x approaches a be always equal to the value…

A: Find your answer below

Q: 6. Find the absolute extrema of the function on the closed interval given: f(x) = 2x/2 – x; [ –2,1]

A: Pue derivative zero, if value lie in interval then put in function for maxima and minima

Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

A:

Q: Express the domain of f(x) = v20 – 7x using interval notation. Use oo for o. Domain of f(x) is…

A:

Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

A:

Q: Which of the following family of functions are not known to be globally continuous (ie, contin- uous…

A:

Q: Let g be a function with domain the rational numbers, defined byg(x) = 2/x - √,2for rational x. Is g…

A:

Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Given that limx→∞ x2+1x+1. Compute the limit as follows.

Q: sketch the following rational functions by determining all critical values. h(x)=x2-2x-8/x2-9

A: To evaluate the critical points of the rational function h(x) = 0 we must solve the equation h'(x) =…

Q: ind the intervals where f(x)= x3-2x2+8 is increasing and the intervals where it is decreasing

A: Given query is to find the interval where f(x) is increasing and decreasing.

Q: 4. Find the intervals in which the function f(x) =x³ – 6x2 +9x +30 is concave up/concave down. Also…

A:

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

A: we have to find the intervals on which f(x) is increasing and the intervals on which f(x) is…

Q: 2. Locate the absolute extrema of f(x)=-5e¯* on the closed interval (-00,00).

A:

Q: If f(x)<0 for all real numbers x, then f is decreasing on(-♾,♾) True or false

A:

Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

A:

Q: Find the intervals of monotonicity of the function f(x) = 4.

A: Intervals of monotonicity means we have to finds intervals in which function is inreasing or…

Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: find the absolute extrema of f(x)= 4x^2-48ln(x) on the interval [.4, 5]

A: Given function is  f(x)=4x2-48ln(x) Differentiate both sides with respect to x. f'(x)=8x-48x Now,…

Q: Consider the function f(x) = 8x + 4x¯. For this function there are four important intervals: ( – ∞,…

A:

Q: Find the extrema and possible points of inflection (if any exist) of f(x)- In x X

A:

Q: What kind of discontinuity does f(x) = *-3 have at x = 2? X-2

A: A function is said to possess non-removable discontinuity if the limit of the function does not…

Q: 5. Consider two entire functions with no zeroes and having a ratio equal to unity at infinity. Use…

A:

Q: 5. Find the interval on which f(x) = x³ – 3x2 – 144x – 140 is concave up and the interval on which…

A: We will solve the problem

Q: sketch the following rational functions by determining all critical values. f(x)=3x2-x3/x2-9

A: The given function is f(x) = 3x2-x3x2-9,This function is not defined at x = -3, x = 3.We try and…

Q: entiable at x = 1. What is f_(1)?

A:

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

A:

Q: Find the absolute extrema of the function on the closed interval.                   f(x) = 4x / (x2…

A: f(x)= 4xx2+9so,  f1(x)= 4(x2+9) - 4x(2x)(x2+9)2Now equ    f1(x)=0=                4(x2+9) -4 x(2x) =…

Q: Consider the function f(x) = 7x + 5x¯¹. For this function there are four important intervals: ( − ∞,…

A: We are given the function for which we need to find the stationary points f(x)=7x+5x-1

Q: x' - 8 24. f(x) : x? – 4

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.