x-x +4 x <0 h(x) = {Ix – 1| +3 0 2, 5. The function h is defined as above for some real numbers a and b. (a) Suppose a=-1 and b =-4. Is h continuous for all x? Justify your answer.

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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: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

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Q: 3. Find the absolute maximum and absolute minimum values of f on the given interval. a. f(x) = 12 +…

A: This question is related to maxima and minima of functions, We will solve it using differentiation.

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x…

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Q: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

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

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Q: 1. Find the absolute maximum value of the function f(x)=x³ – x² – - x on the interval -1<x<10.

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Q: x- 1 f(x) = x + 2 %3D is continuous at x = 3.

A: Check function is continuous or not at x=3

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Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: 6. Find the absolute extrema of the function on the closed interval given: f(x) = 2x/2 – x; [ –2,1]

A: Pue derivative zero, if value lie in interval then put in function for maxima and minima

Q: 1. Find the absolute extrema of f (x) = x* - 8x² + 3 on the interval [-1,3].

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Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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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…

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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: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

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Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

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Q: 7. Find the absolute maximum and minimum of f(x) = x!/² ( on the interval [0, 4]. %3D

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Q: The function f(x) = 3 x4-4 x3-12 x2 +1, is decreasing on the interval OA (-00,-2)U(0,2) OB…

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

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Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

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Q: 1. Does there exist a differentiable function f that is continuous on the closed interval [1, 4],…

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Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) f'(x) > 6 for all x. = -2…

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Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

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Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

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Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

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Q: Find the absolute maximum and absolute minimum of the function f(x)=x^3-18x^2+96x+150 on the…

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

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Q: 11. Determine the absolute extreme values of f(x) = xe-/2 = xel-/2 on the interval [0, 5].

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Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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