Suppose that 2 ≤ f '(x) ≤ 4 for all values of x. What are the minimum and maximum possible values of  f(5) − f(1)?  ?≤ f(5) − f(1) ≤ ?

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: Find the critical numbers of the function. (Enter your answe g(x) = x² In(x) %3D X =

A: We find g'(x) using the product rule. g(x)=x2ln(x)g'(x)=2xln(x)+x21xg'(x)=2xln(x)+x

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: -x²+5 < f (x) < x+1 2

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Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

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Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

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Q: On the graph of f(x) = cos x and the interval [27, 47), for what value of x does f(x) achieve a…

A: Here given function

Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given: f(x) is a function continuous for every value of x whose first derivative is f'x=21-x1+x2 and…

Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: Find the absolute maximum and minimum values of ƒ(x) = x2 on[-2, 1].

A: Given,  fx=x2 on −2,1

Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: What are the critical points of the function f(x) = 1

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Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: What is the absolute minimum value of p(x)=2x^2+x+2 over [−1,3]?

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Q: for what value of x does the function  f(x) = 1/3 x3 - 4x attain the absolute minimum in the…

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Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

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Q: Find the absolute minimum value of f() = xe on [-5,0].

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Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: The interval where  f(x) = )=(√x+2) / x2 - 2x - 8 is continuous is ?

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Q: (7) Does the extreme value theorem tell us that f (x) = ! has an absolute maximum and absolt minimum…

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Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

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Q: Find the absolute maximum and minimum of f(x)=3x^3-x+1 on the interval [0,1]

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Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x &lt; 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Find the absolute maximum and minimum values of f(x) = (x² + x)i over the interval [-3, 4]. absolute…

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Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: Suppose that for all x ∈ R f ′ (x) > 0. Let h(x) = f(2x − x^2 ) for all x ∈ R. Then on [3, 5] where…

A: h(x) = f(2x - x2) Then h'(x) = (2 - 2x)f'(2x - x2)                     = 2(1 - x)f'(2x - x2)…

Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: 2) Find the absolute minimum value on (0,∞ ) for 4 f(x)= 5+x+

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: We know,  -1≤cos x≤1 for any real value of x.

Q: Suppose f is differentiable with f(0) = 0 and 0 0.

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Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

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Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

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Q: If f(x) = x² + k find k so that f has a critical number at x = 3. %3D

A: To find the critical number for any function fx we have to solve the derivative f'x=0. That is we…

Q: If f:[0, 3] → R is continuous, must its range be a closed interval?

A: If f:[0, 3] → R is continuous, must its range be a closed interval