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

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: The function f(x) = x* - 18z is increasing on the intervals

A:

Q: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: If function is continuous  Then, it will be continuous on x=-1 and x=12 Therefore, limx→-1-1fx=f-1…

Q: 1 1

A:

Q: Find the intervals on which f(x) = x4 is increasing  and the intervals on which it is decreasing.

A: Given function:

Q: a)= 3ス2-3 %3D

A:

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

A:

Q: Find the global extrema of f(x)=√5−4x on the interval [−1,1].

A:

Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

A:

Q: 2. Suppose that f is an increasing function on the interval [a, b]. Let F(t) = %3D a.) Argue that if…

A: suppose that f is an increasing function on the interva a,b let Ft=∫0tfxdx (a) if a&lt;x*&lt;b then…

Q: 4. List the discontinuities for the function f(x) = cot(* :).

A: First write the given function into Numerator and denominator form and , to find the discontinuity…

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: On what domain is the function f(x)=1+√−6−3x continuous?

A:

Q: Prove that the following function is continuous on the interval [-5,5]: H(x)= the square root of…

A: Given, H(x)=25-x2we have to prove that the given function is continous on the interval[-5,5]…

Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: +1 Differentiate the function f (x) = In +1

A:

Q: Find the absolute extrema of the function on the closed interval.                   f(x) = √x − 2,…

A: Given function:

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: I am haiving difficulties finding the global max and min for th function f(x) = (3x^(1/3))−x on…

A:

Q: Find the absolute extrema of the function on the closed interval.

A:

Q: Suppose ƒ is an odd function,Evaluate function

A: Given:∫04 fx dx=3,∫08 fx dx=9∫-84 fx dx=?Odd function:∫-aa fx dx=∫-a0fx dx +∫0afx dx=-∫0afx dx +∫0a…

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

A:

Q: from x = 1 to x = 4 2

A:

Q: Locate the absolute extrema of the function on the closed interval. f(t) = ₂, [3,5]

A:

Q: Show that the function is discontinuous on R. f(x) = { 1; 0; for x € Q for a Q

A:

Q: У S 1 X

A: The function is said to be increasing in an interval if its value increases as the value of x…

Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

A:

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

A:

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: Find the interval on which f(x) =x'e is increasing.

A: We find f'(x) using the product rule

Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

Q: F:[- 2,2]– R, F(x) = L((- 3(² + 1) dt

A: We have F(x)=∫-2x2(t-3)(t2+1)dt       Apply Liebnitz's rule for differentiation under integration…

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Make a graph of the functionƒ(x) , for x ≥ 1. Be sure to include all of the evidenceyou used to…

A: Given:  The function fx=∫1xdtt for x≥1, To sketch: The graph of fx for x≥1,

Q: 3. Give an example of a function f.N→N which is surjective but not injective.

A:

Q: Find the open intervals on which the function is increasing y = x/100 – x²

A: A function is said to be increasing in an interval its derivative is positive in that interval.

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: 26) The interval where f(x) is decreasing is?

A: Answer and explanation is given below...

Q: On what intervals is the function f(x) = x-4r both decreasing and concave up? Write your answer in…

A: fx=x4-4x3 Differentiating with respect to x, we get f/x=4x3-43x2    ∵dxndx=n·xn-1=4x3-12x2 Again…

Q: Determine the interval(s) on which the function is (strictly) decreasing.

A: We need to find the intervals on which the given function is strictlydecreasing.

Q: 5. Use the graph of the function f(x) below to estimate the open interval(s) on which f(x) is…

A: As per our guidelines, we are allowed to answer only one question. Since, u have posted multiple…

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

Q: 5. Is the function given by g(x) = 4x³. 6x continuous on R?

A:

Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

A:

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.