Does f(x) =x3 -1 on [-1,1] satisfy the conditions of Rolle's the Rolle's Theorem. Justify your answer. value that satisfies

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: Find all critical points of the function f(x)=x√1−x2.

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Q: Find all critical points of the function f(x) = x4 – x-

A: Critical point is 5/4 Explanation is given below

Q: Show analytically that the function f is not differentiable at x = x² x1

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Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: (a): Find the critical points of the function f(x) 6x2 12x. (b): Apply Rolle's theorem for the…

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Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Find all the critical numbers for the function f(x) = (x-1)/(x+1)

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Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

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Q: Differentiate f(x) = f'(x) = 2 ax with respect to x. Assume that a and k are positive constants. k+x

A: To differentiate fx=ax2k+x with respect to x. Assume that a and k are positive constants.

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

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Q: Verify Mean value theorem for the function f(x)=4x3+x+2 over t interval [0,1].

A: Prove hypothesis of mean value theorem Differentiate continuous and value of c

Q: Can Rolle's Theorem be applied to f(x) = 1/(1-x) on interval [0,3]? If yes, what is c in (0,3) such…

A: here we can't apply the rolles Theorem

Q: Find the value of “c” guaranteed by the MVT theorem over the interval [-8,-6] for the function: F(x)…

A: Given function is : Fx=2x3+9x2-60x        -8,-6 To find the value of c.

Q: Find the positive critical point of the function f(x) 2+3

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Q: Consider the function  f(x) = (x − 4)/( x + 2) .…

A: We have to say about the critical number 2 for the function: fx=x-4x+2 We know that we do calculate…

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<0 for all points x,y.   To determine: Whether…

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

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Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Find all critical points for the function f(x)= x²e!-2¤. %3D

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Q: 1. Consider the function f(x) = sinx - e-* has a root in the interval [0,1]. Use false position…

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Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function -5x f(1) = | V1+ tª…

A: To differentiate the function by using first fundamental theorem of calculus f(x)=integration (x to…

Q: Find all the critical points of the function f(x) = x^3 - 2x^2 - 15x + 2 on the interval [-1, 3]

A: Let's find.

Q: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

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Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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

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Q: Find all critical numbers for the function f(x) = zt_ z궁 || -

A: The function is given by fx = x13-x-23 To evaluate: The critical numbers of the function.

Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: To find the critical numbers, first find the derivative of f(x) then set the derivative equal to…

Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

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