Find the constants a and b such that the function is continuous on the entire real line. f(x)=    6, x<=-2 ax+b, -2=4 a =  b =

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 values of the constants a and b, that make the function f(x) continuous everywhere. (2x3 + x +…

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Q: Find the absolute maximum and minimum of f (x)=x* – 2x -x - 4x +3 on the closed interval [0, 4]. а.…

A: fx=x4-2x3-x2-4x+3 Differentiating wrt x, we get  f'x=4x3-6x2-2x-4 Putting f'x=0, we get…

Q: Find the number in the interval [−1, 1] such that the sum of the number and its square is a maximum.

A: Given: The given interval is -1,1. We have to find where the sum of the number and its square is a…

Q: 1 x, and the line perpendicular to 6 Find the area of a triangle bounded by the y axis, the line f…

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Q: The absolute minimum value of the function f(x) = 7x2 - 14z +9 over the interval [0, 8] O 10 O 2 O…

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Q: Find numbers a and b so that f is continuous at every point.

A: Given,

Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x&lt;1We have to find constant a such that the function is…

Q: (a) Find all the critical points, extreme values, interval of concavity and the zeros of the…

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Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

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Q: Find the absolute extrema of the function on the closed interval.

A: Find the derivative for g(x).…

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: For f (x) = 3x2 – 4x + 2, (a) find the absolute maximum and minimum on [-2,2] using Calculus %3D

A: The points of local minimum and local maximum can be obtained by differentiating the function and…

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Find the constant a such that the function is continuous on the entire real line. (x) = {4x?, ах —…

A: We have to find a

Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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

A: Given,             f(x)=3x2-4x-3

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Find the constant a such that the function is continuous on the entire real line. 9x², ax - 3, a = x…

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Q: Find the area of the region bounded by f(x)=-x^2+6x-5, the x axis, and the lines x=2 and x=5. Graph…

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Q: Find the absolute maximum and the absolute minimum for: a. f(x) = 10x on the interval [-1, 2]. b.…

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Q: 13 X ƒ(x) = [5,-3],ƒ(c) = -1/ x²-4,

A: The intermediate value theorem states that if f is a continuous function whose domain contains the…

Q: Find numbers a and b, so that f is continuous at every point.  f(x)= 20 , x-1

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

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Find the absolute maximum and minimum values on the interval: g(x) = In(x² + 6x + 20), [-5, 1]

A: Let  be a function defined over an interval  and let  We say  has an absolute maximum on  at  if…

Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function

Q: Solve for a and b that makes the function continuous at every number in its domain f(x) = 2x+1 x5

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Q: Find the greatest and least values of f(x) =x' –- 3x² +1 on the interval of [-3,2]

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A:

Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: Find the constant a such that the function is continuous on the entire real line. 3sin x if x < 0…

A:

Q: The absolute max for the function f(x)=x2 – 2x+1 on the interval [-2, 3] occurs at : Select one: а.…

A: Given function is  f(x)=x^2-2x+1

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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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: Find the absolute extrema of the function on the closed interval. f(x)=x3+6x2, [-6,1]

A: To Determine: Find the absolute extrema of the given function on the closed inteval.…

Q: Find values of the constants a and b, that make the function f(x) continuous everywhere. 2x3 + x +…

A:

Q: Find the x-coordinate of the absolute maximum of the function f (x) = x³ – x² – x +1 on the interval…

A: Given

Q: . Find the absolute maximum and minimum values of f(x) = 2x3 − 21x2-21X 2+ 60x + 1 on the closed…

A: We have f(x) = 2x3 - 21x2 + 60x + 1 We find its derivative w.r.t. "x", f'(x) = 6x2 - 42x +60 To find…

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: Find three positive numbers x, y, and - whose sum is 15 and product is a maximum.

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Q: Find the values that make the piecewise function continuous: 2, XS-1 f(x) = ax + b, -1<x< 3 x2 3 -2,

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Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

A: For a function to be continuous, the value of the left and right limits at critical point needs to…

Q: 7+6z – zº x 4 тх + b,

A: Given that,    A function is continuous everywhere means the function is continuous at every point…