Is it true or fase ? There is a number c in the interval (a, b) such that f(c) = 0.

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: Describe the long run behavior of f(x) - 2? As x → - 0o, f(x) → ? As x → 0, f(x) → ?

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Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

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Q: Let f(x) = V6 – x and g(x) = a? – æ. Then the domain of f og is equal to

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Q: If f"(x)>0 on an interval I then...

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Q: For what value of the constant c is the function f continuous on the interval (-,00). Sa? – 3, x с…

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Q: What are the values of a and b that make f(x)=ax+a+b+1  x>0 continuous and differentiable

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Q: Let f : R" → R with f(x) = /1+ ||x||?. Show thatf€ C.

A: As per the question we are given a multivariate function f from Rn to R , and we have to show that :…

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: f(x) = (x − 6)3 + 4 is a polynomial function. This is continuous for all values of x. So f(x) will…

Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

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Q: Consider the function f (x) = 3x² + 2x – 4 What is the exact value of Cin the interval [-2, 4] such…

A: By using Mean Value Theorem for Integrals f(x)=3x2+2x-4 find c over interval [-2 , 4] = ?

Q: What are the domain and range of g(x) = 3√x+4? OD: [3,) and R: [0, ∞) OD: [4,) and R: (-∞, 0) OD:…

A: The given function is: g(x)=3x+4

Q: Explain why you can not apply the mean value theorem to the function f(x) = x2/3 on the interval…

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Q: Find the constant a, or the constants a and b, such that the function is continuous on the entire…

A: Given function is f(x)=x3, x≤2ax2,x&gt;2

Q: At what points c does the conclusion of the Mean Value Theorem hold for f(x) = x³ on the interval…

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Q: Let I be the interval disjoined from {-1,1} .Prove that the function f(x) = x+(1/x) is…

A: Given that I is any interval disjoint from [-1,1]. Let I=(-∞,-1)∪(1,∞) f(x)=x+1x To show f(x) is…

Q: (a) Verify Rolle's Theorem for f(x)= 3x – 12.x + 4 over the interval 0, 2

A: Verify rolle's theorem

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: The Intermediate Value Theorem that states if a function f(x) is continuous and k is any number…

Q: 4x 82. f(x) = X - 3

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Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Find the intervals on which the function f(x)=x3+ax+b (where a,b are any real numbers) is convex…

A: Given function is firstly, we find f''(x)

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: Find the interval in which the function is positive. f(x) = x2 - 7x + 10 %3D I. (- , 2) II. (2, 5)…

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Q: 2. Determine the interval(s) where F(x) is increasing. Justify your answer.

A: 2.According to the graph of function f(x ) is defined as   f(x)=x+2     -5≤x≤-24-x2   -2≤x≤232x-3…

Q: The range of f(x)= 3+|x| is O (0,3] O (3,0) • 13, x) O (-x,3) 1Tx,3] (-x,3]

A: Explanation of the answer is as follows

Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: 21. What is the domain and range of f(x) = V– In x ?

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 81. f(x) = |x – 5|

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Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

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Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: (c) For what values of a and b does the function ах — 3, x < 4 f(x) = (-x² + 10x – b, x2 4 satisfies…

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Q: Given the function of f(x) = -3 – in the interval [-8, –2], find a point x = c between -8 and -2 so…

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Q: 1. Why is f not a function from R to R if a) f(x)= 1/x? b) f(x) = T? c) f(x) =±V(x² + 1)?

A: We'll answer the first question since the exact one was not specified. Please submit a new question…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

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Q: Describe the long run behavior of f(x) = – x² - As x → – ∞, f(x) → ? V - As x → ∞, f(x) → (? V

A: Describe the long run behavior of f(x)=-x5As x→-∞, f(x)→?As x→∞, f(x)→?

Q: Let f(x)=x in(x). Find the interval on whichfis increasing. (a) (0, o) (b) [e¯ !, ∞) (c) [1, ¤) (d)…

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Q: over what domain interval is f(x)=|x| increasing?

A: Consider the given function fx=x

Q: let f(x) = on interval 0<x<2n, find a 2

A: See the attachment

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: fx=x2+xx-1, 52, 4,  fc=6 Given function is continuous in the interval 52, 4. Now,…

Q: f(x)=(x-6)³+4, [4,7],f(c)=3 3

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Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

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Q: How do I state the numbers and reasons at which f is not diffrentiable?

A: First check whether the function is differential or not. This can be done using the differential…

Q: On which interval is f(x) = x – 12x + 12 decreasing? o (-2, 2) o (-00, 2) o (-0, -2) U (2, +0) ㅇ…

A: Let's find.

Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

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Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =…

A: Given: f(x) = 1/(x − 3) and f in on interval [0,6]

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = -x² + 10x - b, x2 4 satisfies…

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