28. Find the value of a that makes the following function differentiable for all values of x. if x< 0 ax g(x)= x2-15x if x 20 The function g(x) is differentiable for all values of x when a= (Simplify your answer.)

Q: (i) Discuss the continuity of the function f(x)= x^2-3x        if x&lt;2…

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Q: b) Suppose that f(x) = }Bx + 2 SBx² – 3 if x 2 Find the value of ß so that f(x) is continuous…

A: The given continuous function is,

Q: For what value of the constant c is the function f continuous on (-∞, ∞)? ( cx2 + 2x x3 - cx if x <…

A: We know that for any value of c, for x &lt; 5, the function is continuous and for x &gt;= 5, the…

Q: 1 If f(x) = and g(x) =-, 2x +1 1 find f (g(x)) and its domain. - 2

A: Composite function :  A composite function is created when one function is substituted into another…

Q: 2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0…

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Q: 1) Find all relative extrema in the function f (x) = x 3 + 3x2 – 24x + 12.

A: For relative extrema the derivative of the function will be zero. Thus,…

Q: 1) Find all relative extrema in the function f (x) = x³ + 3x2 – 24x + 12. 2) Find all points of…

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Q: Answer the following questions for the function f(x) = x/x² + 4 defined on the interval -7 < x < 5.…

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Q: you agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

A: Yes i agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

Q: 4. State all the values of x in which f(x) is not differentiable. Justify your answer. b) f(x) = - 2…

A: Given: 4. State all values of x in which f(x) is not differentiable.(a) From the graph given above…

Q: Suppose f and g are functions that are differentiable at x=5 and that f(5)=8 ,f'(5)=-3 ,g(5)=-1 ,…

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Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: 2. Evaluate whether the following initial values is true in the function: y = 4cos-+ e-2x 2.a) 2.b)…

A: Given , y=4 cosx2+e-2x

Q: ,if x>2 Find the correct value of bb that makes

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Q: 3.4 Differentiate f(x) = a°x* - 5ax with respect to x. Assume that a is a constant. f'(x) =D

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Q: 17. Given the function f (x) = x2 + 2. Find and simplify the difference quotient. S(x+h)-f(x) h 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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: onsider the function: h(x) = 5 for x ≤ -4  2x+ 6 for -4<x<2 5- x2 for x ≥ 2 (D) h(−1) (E) h(0)…

A: Since you have asked a question with multiple question in a single request, we would be answering…

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

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Q: 3. Consider the following functions: f(z)) = x² + 16 9(=)) = (x – 16)² h((x)) = (x + 1)² – 16…

A: Given: f(x)=x2+16g(x)=(x-16)2 and h(x)=(x+1)2-16

Q: Answer the following questions for the function f(x) = x/x² + 36 defined on the interval – 7 < x <…

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

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Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

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Q: Suppose that g is a function that is differentiable at x = 4 and that g(4) = -2 and g' (4) = 1. Find…

A: We are asked to find the value of h'(4)

Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: Answer the following questions for the function f(x)=xsqrt(x^2+36) defined on the interval -4≤x≤5.…

A: solution is given below..

Q: For what value of the constant c is the .! function f continuous at x-3 |cx – 2 , if x 3 2 -1 -2 1

A: If function is continous then,limx→n+ fx =limx→n  fx = fnat point nso at given point x=3limx→3+ fx…

Q: (i) Discuss the continuity of the function f(x)={x2−3x if x&lt;22x+4 if x≥2 on the open interval…

A: Part (i):   In the region x &lt; 2 the function is defined as x2 – 3x. This polynomial is continuous…

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f(x). If f(1)= 5 and f'(1)=10, then…

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Q: 1) The function f(x) = x + 4 is odd True O False

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: [kx, if 0 sx <2 For the piecewise function fx) = {2k, if 2 <x < 4 k- x+ 5, if x + 4 determine which…

A: if piece waise function is continuous at connecting points then piecewise function is continuous at…

Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

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

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Q: Q1.Given: x2 - 4 when x 3 1.Find what values of ( a) and (b) that will make the function continuous…

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Q: х2 — 4 3. Do you agree with the contention that the functions f(x) = x + 2 and g(x) х — 2 are the…

A: f(x)=x+2 gx=x2-4x-2=x-2x+2x-2=&gt;gx=x+2

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

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Q: 10 Q4 For the functions f(x) = 7x + 4, h(x) =-3 and g(x) = 3x-2 (a) Evaluate (1) g(4) (ii) h{g(4)}…

A: It is given that fx=7x+4,  hx=10x-3,  and  gx=3x-2. (a) Evaluate: (i) Find the value of g4.…

Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: Where is the function undefined and where is it equal to 0. f(x)=3e^2x-3

A: We can solve above question both through algebra and also through drawing it's graph. Both of them…

Q: 38. At what value of x should the function f(x) = In(x – 4) approach to so that f(x) will be as…

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Q: (Bx2 – 3 Bx +2 if Suppose that f(x) = x< 2 if Find the value of ß so that f(x) is continuous…

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Q: For what value of the constant c is the function f continuous on (-00,00) f(x) =Cx+4cx+5 ifx<1…

A: Here we have to find the value of constant c for which the function is continuous.

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

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Q: Suppose f(x) =x++x³ – 6x2. Determine the value of x where f has a relative maximum value. O x= - 2…

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Q: For what value of the constant b is the function f continuous on (- 0, ∞) where x2 – 36 if x 6 1 6…

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Q: 1 You are given the function f(x) = x2+7 f(x) is concave up whenever:

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