Consider the function f(x) = i + x². How does this function essentially behave for large positive and negative x-values? Use this to sketch the end behavior of the function.

Q: Let f(x) = x2 – 2.x. Use the definition of the derivative to calculate f'(3) %3D -

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

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Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

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Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: Find the derivative of the function. f (x) = = 4 %3D 12 - 12 - x2 0 4

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Q: Select the correct answer for end behavior of the function: As a → -0, ƒ(x) → As x → 0, f (x) →

A: we have to check

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 points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

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Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

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Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: We have to determine the relative extreme values of the function using the first derivative test.

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: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. x2…

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Q: Let f(x)= 3x^2+x-5. Using the definition of the derivative, find f’(x).

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Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: Use the product rule to calculate the derivative  f(x)=x^3(2x^2+1)

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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: Determine where the function f(x) = √ x / x + 1 is increasing and where it is decreasing.

A: fx=xx+1

Q: The function f(x)=(2-x)/(3) is continuous at

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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: Use the formula  to find the derivative of the function

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Q: Differentiate the function. f(x) = e2 f'(x)

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Q: Use the first and second derivatives to obtain sketches of the function below. 3 1. f(x) = 3x° –- 9x…

A: Given: Function f(x)=3x2-9x+1

Q: Find the derivative. f(x) = 4/6x +7 f'(x) = %3D

A: As we know thatddxxm=ddxxm2=m2xm2-1

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: h(x) = In(v2x +4) %3D

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Q: Find the first and second derivatives of the function. f(x) = √3x-7     f '(x)=   f ''(x)=

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Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: Find the absolute maximum and minimum of the function  f(x)=xe-x on  the interval [-1,1]

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Q: 1, Differentiate the function. (7) f(x)= e (8) f(x)= (9) f(x)= Vx+/2x+ V2x (10) f(x)= 81+

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Describe the process of linearization of a function f(x) at a point x = a, and explain how it can be…

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Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x<0 Thus, the left hand…

Q: Use the Product Rule to find the derivative of the function. g(x) = (x² – 6x + 7)(x³ – 1) g'(x) =

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Q: A once-popular dog’s chew toy is slowly declining in popularity. The quartic function…

A: Given that x is the number of years since 1993 So 2001 means x=2001-1993=8

Q: Differentiate the function with respect to the independent variable. f(x) = 2x° In xº f'(x) =O

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Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: Differentiate the function. g(x) = In(xe-Sx)

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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: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: Find the derivative of the function f(x) = 8x² – 14x by the definition of derivatives f(x+h)-f(x)…

A: Given function: fx=8x2-14x

Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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Q: sketch the curve f(x)= ln((x^2-4)/(x^2-3x-4))

A: given curve is                                                     f(x)=lnx2-4x2-3x-4 we have to…

Q: find the derivative  f(x)=x2(x3-1)

A: Apply the product rule and obtain the derivative of the given function.

Q: Find the derivative of the function f(x) = 9x-³ + x² + 14. f'(x) = %3D

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Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 − 4x + 2)(x3 − 5)

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Q: Rewrite the function g(x) = ((x^2)-1)/((x^2)+2) so that you can solve for the derivative using the…

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Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

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