4 If f(x) is one- to - one function , describe the h(x). fla) # Is it * also one-to - one function , discuss it.

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: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

A:

Q: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: 50. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Given: fx=3x-2 Concept Used: Linear function is continuous everywhere.

Q: 9. If a continuous, differentiable function f has values f(-2) = 3 and f(4) = 1, what can you say…

A: Give that: f(-2) = 3 and f(4) = 1

Q: A function is defined by: In( x- 1) f ( x) =- 1-x

A:

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 f'(x). f(x) = x5 – 2x3 + x – 1 %3D f'(x) = Compare the graphs of f and f' and use them to…

A: Given: f(x)=x5-2x3+x-1 To find: f'(x)

Q: Find the number c which will make the function continuous on (-00, 00). x< 2 f(x) = x+ c, x22

A:

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A:

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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 x-value(s) where the function f(x)- xS2 is not differentiable x-1 x>2 Give a reason for…

A: Consider the given function fx=xx2-1,    x≤2x-1,        x&gt;2. Sketch the graph of the given…

Q: Page < 11. Use f'(x) = lim x+h)-f(x) to find the derivative of f(x) = x² + 3.

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

Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

A:

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: Let f be a function. Explain, using any method , as to why f(x) and f(x) + 2 have the same…

A:

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

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 f '(x) for f(x) = In x - %3D www f '(x) = www

A:

Q: Find the open interval(s) where the function is increasing and decreasing. f(x) = - x + 3 Show work…

A: For a function f(x): f(x) is increasing in the interval where f'(x) &gt;0 f(x) is decreasing in the…

Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

A:

Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: The equation of the tangent line to the graph of a function f at (3,) is y(x) = x + 1. What is…

A:

Q: A closed rectangular box is to have a square base and a volume of 60 ft3. Letting x denote the…

A: Given that volume of ractangular box is 60 ft3and square base having side = x height =yTo find :…

Q: A function fC) is defined as f) = --Sr. What is f(-3)? %3D

A: Explanation of the solution is given below..

Q: The point (2,f(2)) is an inflection point .1 for the function f when f(2) = 0 %3D

A: Given statement,            The point (2, f(2)) is an inflection point for the function f when…

Q: 2) If possible, give an example of where a function is continuous at a point but not differentiable…

A: Continuity of a function is the characteristic of a function by virtue of which, the graphical form…

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

A:

Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

A:

Q: even function of x if f(-x) = f(x) symmetry about x-axis Other:

A: Even function of x if f(-x)=f(x), symmetry about x-axis (A) True (B) False (C) Other

Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

Q: Let us try to find where a function is increasing or decreasing given the following. 1. y = 2x –…

A: A function of x is given.We need to find the function is increasing or decreasing in the given…

Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: How can we verify the natural domains and associated ranges of some simple functions?

A: let f:X→Y be any function from a non-empty set X to a non-empty set…

Q: Find f"(x) if f (x)=√√5 - 4x. Show work:

A:

Q: If f is even and differentiable function, the x = 0 is a critcal number of f. True or False

A: Known fact: For even differentiable function, 0 is a critical number.

Q: prove two Function invezse each other fk)= (x-2)

A:

Q: Use second derivative test, If f(x) = 36x + 4 then f(x) has a local 3 maximum at the point O x = -7…

A: Here we need to find the local maxima of the function.  The solution is following .

Q: 3. Use the limit definition of derivative to find f'(x) for f (x) = You will only get credit for…

A:

Q: What are even and odd functions of symmetry? For example f(-x)=-f(x), f(-x)=f(x), Symmetric about…

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Q: f(x)=√√x at x = 7

A:

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: Can the Mean Value Theorem be applied to the function f(x) = 1/x2 on the interval [−2, 1]? Explain

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Q: Identify three cases for a function NOT to be differentiable at a. Explain why each case fails the…

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Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

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Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

A:

Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…