2. The function ƒ is continuous on the closed interval [-3,3] such that f(-3) =4 and f(3)=1. The functions f'(x) and f"(x) have the properties given in the table below. -3

Q: Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local…

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Q: Suppose f is continuous on an interval containing a critical point c and f 1c2 = 0. How do you…

A: The critical point of  f is x=c and f'c=0.

Q: Consider a function f with domain {x|x 0} and the following derivatives: f'(x) = x2 4x - a and f"…

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Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: 2. Find all critical points of the function f(x, y) : = x cos y + sin y + 1 and determine their…

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Q: If the derivative of the function f (x) is f'(x) = 18z2 + 2x + cos(z) + 6, then which if any of the…

A: Solve the first order differential equation by separation of variable and integration.

Q: For the function f(x) = cos2 x on [0,pi]  a) find the critical points on the given interval b)…

A: Given:

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: For what value of the constant cis the function f continuous on(-0,0) x2+ 2x +6 if xsZ cosin (x-2)…

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Q: three times differentiable function f with f (x) 0 has a D derivative at x given l A x) = f(x)--(70)…

A: To analyze the D-derivatives (as per definition) of functions

Q: )=x+- at x = C at x = 0

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Q: The second derivative of the function f is given by f" (x) = esin z (2 cos x – x sin x + xcos?x).…

A:

Q: If f(x) =- 2-cos(x) sin(x) then the absolute minimum of f on the TI 3T is: interval O 2/2-1 O 2/2+1

A: Steps to find the absolute minimum value : Find the critical point of f Evaluate the function…

Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

A:

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: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

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

A:

Q: 1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >1…

A: A function f is said to be continuous at a point x=a if limx→af(x)=f(a).  The left hand derivative…

Q: 47. Determine the first and second derivatives of the function f(x) tan" (x² – x +1) tan %3D at x=1…

A: Given: The function, fx=tan-1x2-x+1   To determine: The first and second derivatives of the given…

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: The function f (x) = x' + 1 is continuous in the interval [-,2, 4] and differentiable in the…

A: Solution-

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: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

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Q: 1. Identify all the x-values of the candidates for where you might find an absolute maximum or…

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Q: 4. Find the first derivative of the given function using the Rules of Differentiation: e sin x…

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Q: f(x)= X-I x=1 √x-1 X = 1 1123 -s continuous at x = 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: 1. Consider the function f(x) = v2 – x. a) Use the limit definition of a derivative to calculate f…

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Q: The function defined by x2 if r 0 is continuous at a = 0. Determine the left- and right-hand…

A: We have to check our function is differentiable at x=0 or not

Q: (5) Consider the function g(x) = 5 ln(x + 2) – r. (a) Compute the derivative g'(z). (b) Use the…

A: It is given that, g(x)=5ln(x+2)-x   If a function f(x) is given, then the derivative of the function…

Q: 2-(i) Suppose that we know that f(x) is continuous and differentiable on [6,15). Lets also suppose…

A: 2) Suppose that we knw that f(x) is continuous and differentiable on[6, 15]. Also, suppose that we…

Q: 2. Find the absolute extrema of the function on the closed interval. f (x) = Vx – 2, [0,4]

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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

A: Mean Value Theorem (MVT):   If f(x) is continuous on the closed interval [a, b] and differentiable…

Q: The graph of f", the second derivative of the continuous function f, is shown above on the interval…

A: In this question we have to find which statement is correct according to the given question.

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

A:

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan…

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 +…

Q: Suppose f is continuous on an interval containing a critical point c and f"(c) = 0. How do you…

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Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: 21. Discuss the continuity of : 1 x+ - for x 2 (ans.: discontinuous at x-0,2 ; continuous at x-1)

A: We have to check for the end points.

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: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

A:

Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

A:

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: The critical numbers r = -1 and x = 2 are found from a continuous derivative f(x). Given that the…

A: