81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the graph of y = f(x)?

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

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: A point is moving on the graph of y³ = x². When the point is at (-512, 64), its y coordinate is…

A: Given, A point is moving on the graph of  y3 = x2. When the point is at -512, 64, its y coordinate…

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: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 300-cc organ at a rate of 5…

A: Given: the concentration of the drug carried by  the liquid=0.1g/cc liquid enters and leaves the…

Q: 9) If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Since you have asked multiple question in a single request, we would be answering only the first…

Q: 250 4. Use second derivative test to determine the relative extrema of the function: f(x) = x2 +

A:

Q: - The table below shows the actual sales of a Product X sold by Company Y from of 2019. th Actual…

A: Given information: The data represents the actual sales of a product X sold by company Y from…

Q: 2 - ) at x = 4 1+ x)

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

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: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

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: Differentiate f (x) = (ex + e-x)/(ex - e-x)

A: We have to differentiate the function: fx=ex+e-xex-e-x Here two function are in ratio so we need to…

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

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: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

A:

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

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

A:

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

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: What is the length L of the interval on which the function f(x)=x4e−x is increasing?

A: Given

Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

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

A:

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

A:

Q: 5. What is the definition of the derivative of a function f(x) ?

A:

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: are correct? The function is decreasing on the interval x > 4.

A: According to graph for x&gt;2 slope = dydx increasesSo the function is increasing on the interval…

Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

A:

Q: Suppose that the function y=f(x) is increasing on the interval (-1,5). Over what interval is the…

A: The x-5 is offsetting the input of x. The beginning of the function increase is at x-5=-1 and the…

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

A: topic -derivative

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

A:

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: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

A:

Q: Find the absolute extrema for the function over the specified domain. y = x2 5 over [ – 1, 2] -

A:

Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

A:

Q: 2. Use the second derivative to find the inflection points and the intervals on which f(x) is…

A: For inflection point, Put f"(x)=0. For concave upward, f"(x) &gt; 0. For concave downward, f"(x)…

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

A:

Q: What is the derivative of the exponential function a x, a &gt;0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

Q: Suppose that the function f(x) is concave down on the interval (2,5). Can conclude that the function…

A:

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

A: Answer and explanation is given below...

Q: Is the function continuous from X = -5 to x = 0? This function is made up of four (4) linear…

A: 1. True, the function is continous from x=-5 to x=0 as there is no break in the       graph between…

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: 4. Suppose that the weekly sales S (in thousands of units) t weeks after a new software has been 200…

A: Given weekly sales S after t weeks when a new software has been introduced is given by S =…

Q: When the price of a certain commpdity is p dollars per unit, the manufacturer is willing to supply x…

A: Given  5p2 - 2x2 = 27 where p is the price of a certain commodity in dollars per unit x is the…

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

A: