The function h(x)=(x+3)2 can be expressed in the form f(g(x)) where f(x)=x2, and g(x) is defined below: g(x)=

Q: (a): Find the critical points of the function f(x) = 8x² – 16x.

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Q: The function f(x) =3 x4-4 x3-12 x2+1, is increasing on the interval

A: f(x) = 3x4-4x3-12x2+1f'(x) = 12x3-12x2-24xf'(x) = 12x(x2-x-2)f'(x) = 12x(x2-2x+x-2)f'(x) =…

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 (f - g)(x). f(x)= 2x- 2, g(x) = 4-x

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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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Q: find th domain of the function    h(x)= x-4/x3-25x

A: We are given : h(x) = (x - 4)/(x3 - 25x) We are required to find the domain of the function.

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

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Q: 2-f (x)=x2-2x

A: Given function is f(x)=x2-2x Find the inverse of a given function i.e., f-1(x)

Q: Consider the functions f(x) = x² – 5x + 4, g(x) = x² + 5x + 6 and h(x) = x² + x f(x) g((x) 3 h(x) a)…

A: We can solve this using definition of function

Q: The Range of f(x) = V1-x is 1. [-1, 0) 2. (-, 1] 3. (-0,0) 4. [0, 0) 1 2

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Q: 2. Given that f(x) = Vx+1 and g(x) =x² -9, find |(x) and give its domain in interval notation.

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Q: If f(x)= 2x-and g(x)=3x+1, what is f(x)-g(x)+g(x)²? O8x6+9x2+3x O8x+9x-x O8x+9x2-3x O8x+9x+x

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Q: Find real values of x for which f(x) = 0. f(x) = x3 − x

A: Given: fx=x3-x To find the real values of x for which fx=0. Solution: Put fx=0 and then solve for x.…

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 – 6x² –…

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Q: The function f (x) = 3x² –4x-3 is continuous everywhere.

A: Given,             f(x)=3x2-4x-3

Q: Differentiate the function f(x) = In(6x7 – 4x) + v2 – e3x. - -

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Q: 2 Find f(x)- g(x) when: f(x) = x2 + 1 g(x) = 2x – 5 x² + 3x – 3x x? - 2x + 6 -x? + 2x + 4 x² - 2x –…

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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: 1 Find the domain of the function f(x) V4 - 2x – x²

A: fx=14-2x-x2

Q: Find the absolute maximum and absolute minimum of the function f (x) = x³ – 3x²+8 on the interval…

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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: Let h(x)=f(x)g(x). If f(x)=−2x2+2x+3 and g(x)=−x2−3x−4, what is h′(−1)?

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Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

Q: Let h(x)=f(x)g(x). If f(x)=4x^2+3x+1 and g(x)=3x^2−3x−4, what is h′(−1)?

A: Given: hx=fxgx, fx=4x2+3x+1, gx=3x2-3x-4

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

A:

Q: let h(x) = f(x)/g(x), where f(x) = -3x^2 + 2x + 2 and g(x) = -2, what is h'(x)?

A: Given  hx=fxgxwherefx=-3x2+2x+2gx=-2 To find the derivative of h(x) Quotient rule is to be used…

Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: (a) g(x) = x + 1 x-1 (using the definition)

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: sketch g(x) = f(x + 3) -2. %3D

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Q: 1. If f(x) = 2x – x² and g(x) = |x – 3|, find the value of f(-2) + g(-2)

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Q: Find ao of the function f(x)=(-x)², 0≤x≤ 2π

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Q: Let h(x)=f(x)g(x). If f(x)=−3x2+2x−3 and g(x)=−3x2+4x+3, what is h′(1)?

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Find the critical numbers of the function. f(x) : 6x2 – 9x %3D

A: given f(x)=6x2-9xdiffrentiate the function to calculate critical pointsf'(x)=12x-9

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

A: Please refer the attached image for complete solution.

Q: The range of f(x)= -/2-x² is %3D [-/2,0] O [0,/2] [-2,2] [2, 0) [0,2]

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

A: Use chin rule to differentiate g(x).

Q: The functions f and g are defined by f(x)=x^2 and g(x)=2x, respectively. Which equation is…

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Q: The domain of f(x)=1xf(x)=1x is (−∞,0)∪(0,∞)(-∞,0)∪(0,∞). What is the domain of…

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Q: Let f (x) = 2x and g (x) = 3x² + 1, find(go g) (x). Show your work using the Equation Editor Tool.

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Q: Let f(x) = x2 – 6 and po = 3 and pi = 2. Use Secant method Example: to find p3.

A: Given: f(x)=x2-6, p0=3 and p1=2 To find: Value of p3 using Secant method.

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 absolute maximum and minimum values of f(x) = 10x(2-lnx)

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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: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

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Q: Let h(x)=f(x)g(x) where f(x)=2x^2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

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Q: x=-2 of f(x)=√x²-1

A: Above question is solved.

Q: Find the extreme values of the function f(x) = (x² + 2x)³ on the interval [-2, 1].

A: