The inverse of the function f(x) = is f-'(x) =_ x + 3 (3x + 4) (1 – æ) (3x – 4) (5 – x) O (3x + 4) (1+x) (1 – x) (3x + 4) o (3x – 4) (1+ æ)

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…

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

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Q: Prove that the function f(x) = x 5 + 2x 3 + 4x − 12 cannot have two real roots. (Hint: Use the first…

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Q: Let f(x)= x2 -3x + In x. Find the local maximum and minimum values of f by using the second…

A: Since, we are given f(x)=x2-3x+ln x and our aim is to find the local maximum and minimum values of f…

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

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Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: Use derivative rules to compute f'(-1) given f (x) = -4x8-32x - 4.

A: f(x)=-4x8-32x-4Formula: xn'=n xn-1

Q: In Problems 23–38, for the given functions f and g, find:(a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘…

A: In Problems 23–38, for the given functions f and g, find: (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g…

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x<5x+1            ,  x≥5

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

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Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

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Q: What is the upper bound of the function? f (x) = 4xª 25x² – 5x = 13 = 4r4 5х -13 --- Enter your…

A: Given : f(x) = 4x⁴ - 25x² - 5x - 13

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: The function f(x) = vx – 2 + V4 – x is – increasing on (-∞, 3) and decreasing on (3, 0) decreasing…

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Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

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Q: Which of these is fixed point equation for f(x) = x*+9x²-x-3. O f(x)=x/(x°+2x) O f(x)=(x+3)/(X+2) O…

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Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: (9) F(<) = { —1, if - п <x<0 1, if 0sxп (h) f(x) — f -х, х, -1<x<0 0<x<1 if if

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Q: if fcx) = _X then f (-1) is: |-X

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Q: 3) f(x) = x--x- 1; [3] [1, -1: 01.4 5) f(x) = 2x² - 2x -1; 4) f(x) = −x- - x + 1; [2, 1 x-1 6)…

A: Average rate of fx change over interval a,b=fb-fab-a

Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

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

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Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1]

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Q: Find f'(x). F(x) = x5 – 4x3 + x - 1 f'(x) = Compare the graphs of f and f' and use them to explain…

A: Given, f(x)=x5-4x3+x-1

Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: 6. Verify Mean Value Theorem for the function f(x) = 3x² -4x +5 in [-1,1].

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Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

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Q: 5) Suppose that f is the function implicitly defined by the equation + tan ( In = evi near the point…

A: Given:       x+y4+ Tanin xy = ey   →1    near the point ( 4, 4 ) eTo Determine: f is an increasing…

Q: 19 – x² ; if x 3 continuous or not on the interval [0, 3].

A: Given function: fx=9-x2;if x≤3x-3;if x&gt;3 The objective is to determine if the function is…

Q: At what points are the functions continuous x -X- g(x) = X - 3 y " 5, x = 3

A: Given:  1. 2.

Q: 4. Differentiate the function. (1) f(x)= in x (2) f(x)= In{x (3) f(x)= In- 2x²(x+2)³ (3x- 2) (4)…

A: HI there, At a time we can answer only one question. So, I have answered first question.

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: Which of these is fixed point equation for f(x) = x*+5x²-x-3. O f(x)=-x = x*+2x²-x-3 O f(x)=|x |=…

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

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

Q: How to solve this problem from webassign by deriving to find f'(x) f(x) = 4x^2 ln 4x

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Q: It works using the second derivative [ osxs] 1. Find the maximum and minimum limits of the function…

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

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Q: Find the average rare of change of the function from x1 to x2 Function: f(x)= x^3- 5x^2-x x-Values:…

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Q: Find f'(x). f(x) = e – x³ arctan(x) -(3 + 3x2 arctan(x) + arctan(x)(3x4)) x2 +1 f'(x)

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Q: Given a domain of (-3,4], the derivative of f(x) = x² exists at x = 4 because 4 is included in the…

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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: x+4 if x2

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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)…

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Q: An even function is one like x2 or cos x. f(x) is even if......... f(x) = finite f(x) = -f(x) %3D…

A: The objective is to select the correct option from the given options.