Let f and g be functions that satisfy f′(2)=−2 and g′(2)=−5. Find h′(2) for each function h given below: h(x)=4f(x)+13g(x)−4=?

Q: Consider the function f(x)=xe−9x,0≤x≤2. On this interval, ff has a minimum value equal to: which is…

A: Given fx=xe-9x 0≤x≤2

Q: b)f(x) = Vx²

A:

Q: Express the given function h(x) =1/(4x + 5) as a composition of two functions f and g so that h(x) =…

A: We need to express the above function h(x) as a composition of two functions f(x) and g(x) such…

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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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: The function h(x)% = can be expressed in the form f(g(x)), where g(x) = (x + 3), and x + 3 f(x) is…

A: Given query is to find the function f(x).

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

A:

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

A: Given: Since every differentiable function must be continuous.

Q: If f(x) =2+|x-3| for all x, then the value of the derivative f'(x) at x= 3 is 0 .a -1 .b 1 .c 2 .d

A:

Q: Consider the function f(x) = -5x* – 11æ³ +x² + 2x – 17. What is the 3 smallest number n such that…

A:

Q: The function h is defined by the equation h (x) = (x – k)², where k is a positive constant. Which of…

A: h(x) = (x - k)2; where k is the positive constant.   y = h(x)   y = (x - k)2 y can not take negative…

Q: I. Solve the following problems on functions. 1. If g(x)= v36 - x² , find g(0), g( - 3), g(=), g(2y)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: 1. a) If f(x) = x-2x + 1 and g(x) =1, find f( g(-2) %3D

A: givenfx=x3-2x+1  and gx=1x2

Q: (a): Find the value of k that makes function continuous at x = 4 f (x) = 7x S2x + 7 x > 4 k x < 4…

A: We will use the definition of continuity at a point to find the value of k

Q: Let f(x) = 5x² - 2²/2 + 8√√x-²3 (a) Find f'(x) (b) Find an equation for the tangent line to the…

A: As we know that; The equation of the tangent line is: y-y0=mx-x0 Where m is the slope of the tangent…

Q: Find the linearization L(x) of the function f(x) : x2 + 4 at x :-1. Answer: L(x)

A: Given:- f(x) = x4 - x2 +4 To find:- Linearization L(x) of f(x) at x= -1

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: b. For what value of (k) is the function y=f(x) continuous at x=3. x3-3x2-4x+12 x#3 x-3 f(x) = k x =…

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Q: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

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Q: The function h() 1 can be expressed in the form f(g(a)) where g(a) (z + 3) and *+3 f(x) is defined…

A: h(x)=1x+3h(x)= f(g(x))g(x)=x+3

Q: Find all critical points of the following function. 3. 3 f(x.y)=- + 8xy

A: To find critical points of f(x, y) we find ∂f∂x and ∂f∂y then equate to zero .f(x, y ) =…

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

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Q: The function h(x) 1 can be expressed in the form f(g(æ)), wher x + 4 defined as: f(x) =

A: The function h(x)=1x+4 can be expressed in the form f(g(x)), where g(x)=x+4 We have to find f(x) = ?…

Q: 8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

A: h(x) is given. We have to find h(2), h(0) and h(-x)

Q: Express the given function h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) =…

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Q: Find the value for k so that the function will be continuous at x = -1. S 9x - 18 l-x² - 4x – 4 + k…

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Q: 7. Find and sketch the domain of the function f(x, y) = 2 ln(49 – x² – y²) + 8/ -

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Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: Find the domain of the function. g(x) = ln(x - 1)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: For the function f(x): X-6 find T (x), the third derivative of f, and f(4)(X), the fourth derivative…

A: Given that:f(x)=x-2x-6To find f'''(x) and f(4)x

Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

A:

Q: Express the given function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that…

A: To Determine:  Express the given function h(x) = (x2 + 2x - 1)4 as a composition of two functions f…

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…

A:

Q: Q1: Find the value of the constant K if the function 4-x ;x#2 f (x) ={3-Vx² +5 is continuous at x=2.…

A:

Q: The function f(x) = x/(x² – 1) is (b) odd (c) not defined at a = 0 (d) neither even, nor odd (e) not…

A: The vertical line test can be used to determine whether a graph represents a function. If we can…

Q: Express the given function h(x) = (3x - 1)4 as a composition of two functions f and g so that h(x) =…

A: Given function,  h(x) = (3x - 1)4 To express the function h(x) as a composition of two functions f…

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

A:

Q: The function h(x) 1 can be expressed in the form f(g(x)) where g(x) = (x + 7) and f(x) is x + 7…

A: Given ,  The function h(x) = 1/(x+7) can be express es in the form f(g(x)) where g(x) = (x + 7)  We…

Q: 1 Use the functions given by fx) 1 and g(x) = x' to find (fº g)¯- %3D X - 125

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Q: Find the absolute maximum and minimum values of f in the given interval. f(x) = x* – 2x² + 1, (-2,…

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Q: Express the given function h(x) = 3√(x2 - 9) as a composition of two functions f and g so that h(x)…

A: Given function is  h(x)= x2-93.

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…

A:

Q: If f(x) is a twice differentiable function with f(0)= 1, f(2) = 4, f'(2) = 5, Then 2xf" ()d =

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Q: Find the domain of the function.(a) f(t)= ln(2t-3)

A: The given function is: f(t)= ln(2t-3) Since logrthmic function is not defined for non-postive…