Show that the function x- 16 - f (x) = x + 4 4 - 10 x = 4 has a removable discontinuity at x = 4.

Q: What is the infinite discontinuity of f(x) = (x^2-3x+2) / (x^2-x) ?

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Q: The function f(x)=12-6x4 has an absolute maximum value of _____________ and this occurs at x equals…

A: Given, Function f(x)=12-6x4

Q: For what value of x does the function f(x) =x³ – - 4x attain the absolute maximum in the interval…

A: Second derivative test: If the function f is twice-differentiable at a critical point x (i.e. a…

Q: The critical point of the function f(x) = a – 6x² + 16x + 13 is %3D - (1, –4) (-2,4) (2, 4) (-2, –4)

A: The critical point of the function y=fx is the point where f'x=0. The power rule of differentiation…

Q: suppose f’(x)=x^4+x^3-6x^2. Determine the value of x where f has a relative maximum value.

A: The solution for the above question is as shown below.

Q: Show that the function has a removable discontinuity at x = 4.

A: A function is continuous at a point x=a if limx→af(x)=f(a). For limit at a point to exist both…

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

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Q: Find the maximum value of the function f(x) = x² . – x within the interval0 < x < 2. -

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

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Q: Can i get help step by step?

A: f(x) = 20 x3 - 3 x5 differentiate f(x) w.r.t  x f'(x)= 60 x2 - 15x4

Q: Find the points of discontinuity of the function f(x)={1−x2,x&lt;0x+2,x≥0 if they exist.

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Q: Show that the function f(x) = Vx4 +3 is even but not odd.

A: The function is even if and only if for any x: f(-x)=f(x)   And the function is odd iff: f(-x)=-f(x)

Q: The function f(x) = x8 + 4x3 –- 7x + 13 has where the absolute minimum occurs, correct to

A: Given, the function        f(x)=x8+4x3-7x+13

Q: Find the value of the constant k that makes the function continuous.

A: Given: h(x)=3x2+2x-8x+2 if x≠-23x+k            if x=-2

Q: Find the absolute extreme of f(x)=x^3-12x on the closed interval [0,4]

A: for finding critical points take f'(x) = 0 then find the function value at the critical points and…

Q: Find the minimum and maximum of the function in the specified interval. 1. f(x) = x² - 6x + 9 on…

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Q: How do you solve question 4?

A: We are given the function, f(x) = x4 – 2x2 + 3x. Here, we need to show that the function f(x) has a…

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

A: Given,             f(x)=3x2-4x-3

Q: Find the function f(x) that satisfies the conditions f1) - | and f'x)= 2x+1

A: Given that: f(x) satisfies f(1)=1and f'(x)=2x+1(x2+x+1)3 We have to find the function f(x)

Q: Determine a point where f(x) has a non-removable discontinuity.   f(x)=x^4+3x+2/x^2−3x−4

A: GIVEN DATA : Function fx=x4+3x+2x2-3x-4        TO FIND : Non removable discontinuity of the fx Non…

Q: 5. Use the Intermediate Value Theorem to show that the function f(x) = x³ + x² – 1 has a zero…

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Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: Show that the function f (x) = -x3 + 2x2 - 6x + 3 is always decreasing.

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Q: Determine all critical points for the function. f(x) = x2 + 6x + 9 %3D

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Q: Find the intervals on which the function f(x)=x3+1x3 is strictly decreasing.

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Q: Determine the value of x of the discontinuous function: х — 1 f (x) 3D {3х — 3 (-4x + 3 x 3 -

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Q: 3. Write down two different fixed-point procedures for finding a zero of the function f(x) = 2x2 +…

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: the function f(x)=x^3-3x^2+5x has neither maximum nor minimum?

A: Consider the given function. fx=x3-3x2+5x Find the derivative of the function. f'x=3x2-6x+5x Put the…

Q: Find the absolute maximum values of f(x) = 2x^3 +  3x^2 + 4 on the interval [-2,1].

A: Given: f(x) = 2x3 +  3x2 + 4

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

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Q: Determine all the critical points of the function f(x) = 3xe3*

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Q: Consider the function f(x)=2x* – 4x² +4. Isƒincreasing or decreasing at the point x - 0.5?

A: Since you have asked multiple questions in a single request, we would be answering only first…

Q: Investigate the continuity of the function at x=3. S-2x +4 if x23 f(x)x-1 fx<3 At x3

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Q: Find the absolute maximum of the function f(x) = xª – 8x² on the interval –1 < x< 3.

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

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Q: Determine the value of x of the discontinuous function: * х — 1 = {3x – 3 -4x + 3 x 3

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Q: Find the local maximum value of f(x)=x^3-27x+8

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Q: Suppose x) =x*+x³– 6x² Determine the value of x vhere f has a relative maxmum value.

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.

A: Topic = Functions

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: Find the value of the constant k that makes the function continuous. 2x - 3x- 20 if x#4 g(x) = x-4…

A: A function f(x) is continuous at a point x = a iff:

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

Q: Use the Intermediate Value Theorem to show that f(x) = 2x3 − 3 has a zero in the interval [1, 2]

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Q: Given the piecewise defined function: 2x - 2 if x 2

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Q: Explain why the function has at least one zero in the given interval.          Function f(x) = x3 +…

A: Given: fx=x3+5x-3