For any function f(r), if g(x) = f(x²) then g(z) is always increasing.

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: The given function is

Q: Given the functions fAx) = x - x and g(x) = x- 1, determine an equation for the combined Ax) y =…

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Q: Find the local and absolute extremum for the functions over their domain: 3. f(x) = x*(x - 2)7

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Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Critical points of the function are the point either the derivative is not defined or derivative is…

Q: The graph of the continuous function g, the derivative of the function f, is shown above. The…

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Q: If f is a differentiable function and such that and g(x) = x+2 / 1+f(x) such that f(0) = -2 and…

A: Given: gx=x+21+fx f0=-2 and f'0=5 We have to find the value of g'0.

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: The function h(x)=1/x−4, can be expressed in the form f(g(x)), where g(x)=(x−4), and f(x) is defined…

A: Given: ------------------------------------------------------------------------------------------…

Q: Find the value of constant K that makes the function below continuous at x = 2. -2x X < 2 X-2 f(x)…

A: Given,           fx=x2-2xx-2 ; x&lt;2kx-3 ; x≥2

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

Q: Find the local and absolute extreme values of the function on the given interval.  f(x)=…

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Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

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Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: Find general formula for f^(n) if f(x)=x^-4

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Q: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: The function f(x)=x2 is decreasing on the interval...................... .

A: Given,f(x)=x2 f(x)=x2 On differentiating both sides w.r.t x we get: f'(x)=ddx(x2)⇒f'(x)=2x Now, we…

Q: 2.) For the functions f (x) = 3x + 5 and g(x) = 2x – 8 find (E) (x) and give its domain in interval…

A: Consider the functions  f(x)=3x+5g(x)=2x−8

Q: Find the local and absolute extremum for the functions over their domain: 1. f(x) = x2 – 6x + 8

A: Given

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 4. Determine the value of the constant k so that f(x) = e* (x + k) decreases on the intervals (- 0,…

A: we have to find value of k

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Over the interval (0,2), the function f(x) = (-x²) e*

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Q: Find a general formula for f (n)(x). f (x) = x−1/2

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Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

Q: The function h(x) ==x-1 represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

A: Please refer the attached image for complete solution. Given : hx=43x-1, hx=fgxfx=2x-1To calculate :…

Q: The derivative of g(x) = (1/2)* is: positive for all x O negative for all x negative for x >0 and…

A: Given function is gx=12x  ....1

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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Q: find the interval on which f(x)=x2-4x+3 is increasing and the interval on which it is decreasing by…

A: The graph is shown below:

Q: If f(x) = 2+|x-3| for all x, then the value of the derivative f'(x) at x= 3 is (A) -1 (B) 0 (С) 1…

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Q: If x is large, which function grows faster, f(x) = 2x or g(x) = x2 ?

A: Given,            fx=2x or gx=x2To find : if x is large, then which function grows faster.

Q: if x 2 1. Determine the constant k such that the function f(x) = is continuous at x = 2.

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions,…

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

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Q: Find f''(x) for: f(x)=ln⁡x/4x

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Q: Determine all critical points for the function. f(x) = (x - 4)³

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Q: nd all the critical points of the function f(x)= ={ x² 23 if x<1 if x ≥ 1

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Q: Determine any critical point(s) for the function f(x)=  -3 / x2 - 9

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Q: if x 2 1. Determine the constant k such that the function f(x) = {1 is continuous at a = 2.

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Q: On the interval 0 < x < 3, the function f (x) = x² – 8x + 16, which one it is  a) is concave down…

A: Given:      y=x2-8x+16 , 0 &lt; x &lt; 3

Q: 3. f(x)=x-x³-x²+1 3

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Find the local and absolute extremum for the functions over their domain: 2. f(x) = x3 + 4x2 – 11x –…

A: Given function is  f(x)=x3+4x2-11x-2

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: Find a simple function g(x) such that f(x) is O(g(x)), where f (x) = (-5x20 + 3)(-3x² – 4x²) + 7(4x²…

A: Given, f(x)=-5x20+3-3x7-4x2+74x2-2.3xx6+4 In In x Therefore,   g(x) is also a function…

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15…

A:

Statements and Logic

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