express the function F in the form f ° g. (enter your answers as a comma- separated list. use non-identity functions for f(x) and g(x).)  F(x)=(x - 1)^7 (f(x),g(x))= (      )

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: 6(x² + 3) ((x – 3)(x + 3))³ 1 -2x f(x) = f (2) = f (x) = (x – 3)(x + 3) ((г — 3)(х + 3))?

A: Since, the numerator is a constant 1, so, the graph has only one horizontal asymptote which is the…

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: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A: Now differentiating with respect to x, we get

Q: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: Differentiate the function.      f(x)  =        ______1______                            In x

A:

Q: Find the absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A:

Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

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Q: f(x) = x2 -4x-2 at x = 1 %3D %3D

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Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

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: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: Use Intermediate Value Theorem and Bolzano's Theorem to show that f(x)=x^3 and g(x)=2x+3 intersect…

A: given functions are                                                     f(x)=x3g(x)=2x+3 if both the…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A: A Function f has a local maximum at a point x0 if the values f(x) of f for x 'near'x0 are all less…

Q: Find the absolute extrema of the function on the closed interval.                      g(x) = 6x2/(x…

A: Given    g(x)=6x2x-2 ;  -2,1

Q: lim 3i 4 +

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Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A:

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 +8x + 15…

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Q: Find the absolute maximum and absolute minimum of the function on the given interval. f(x) = x – In…

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: 6. Find the absolute extrema of the function f (x) = 7x² + 1 on the closed interval [-1,2].

A: We need to check value of f(x) on critical points and boundary values of interval to find absolute…

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

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Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

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Q: the local maximum and local minimum values of f using both the First and Second Derivative Tests.…

A:

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated li f(x) = 4x² –…

A: Given: f(x) = 4x^2-6x

Q: Let be a differentiable function such that f(3)=2.345 and f'(x)= ln(x^2+1).What is the value of…

A:

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using…

A: the given function,  f(x)=-x+22+1,x≤-2x+1,-2≤x≤3x-32-1,x&gt;3

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Find the critical and inflection points of the function f(x) = 4sin³x – 3cos²x

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: How did the function f(x) = -x^3 + e^x - 8 satisfy the intermediate value theorem? Show that f has a…

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Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

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