Check the hypotheses of Rolle's Theorem and the mean value theorem and find a value of...

Check the hypotheses of Rolle's Theorem and the mean value theorem and find a value of c that makes the appropriate conclusion true. Illustrate the conclusion with a graph:

Prove that x^4+6x^2-1=0 has exactly two solutions

Please provide all work needed to solve the problem with explanations. Thank you!

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milcah answered 2 years ago

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = cos(2x), [π/8, 7π/8] (a) Graph the function f(x) = x + 7/x and the secant line that passes through the points (1, 8) and (14, 14.5) in the viewing rectangle [0, 16] by [0, 16]. (b) Find the number c that satisfies the conclusion of...

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 1 − 24x + 4x2 ,[2,4] C=

Does the given function satisfy the three hypotheses of Rolle's Theorem on the given interval? If...

Does the given function satisfy the three hypotheses of Rolle's Theorem on the given interval? If so, determine where f ′ ( x ) = 0 within the interval; if not, explain which hypotheses are not satisfied.

Show step by step to understand 1.Verify that the hypotheses of the Mean-Value Theorem are satisfied...

Show step by step to understand 1.Verify that the hypotheses of the Mean-Value Theorem are satisfied for the function ?(?) = (√(? − 1) + 1) on the interval [2,10], and find all values of ? in the given interval that satisfy the conclusion of the theorem. 2. Verify that the hypotheses of the Rolle’s Theorem are satisfied for the function ?(?) = (?^2−1)/(?−2) on the interval [−1,1], and find the value of ? in the given interval that satisfy...

Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find...

Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem. g(x)=x^3- 9 x^2 + 24 x - 20; [2,5] A)Rolle's Theorem applies and the point(s) guaranteed to exist is/arex= (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B)Rolle's Theorem does not apply.

(A) Find the number c which satisfies the conclusion of the Mean Value Theorem for the...

(A) Find the number c which satisfies the conclusion of the Mean Value Theorem for the function f(x) = x3 -2x on the interval [-2,2] (B) Then use Calculus to find the critical numbers and intervals of increase and decrease for f(x) =(x2+x)1/3

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ). b True or False. The product of two increasing functions is increasing. Clarify your answer. c Find the point on the graph of f ( x ) = 4 − x 2 that is closest to the point ( 0 , 1 ).

Use the Intermediate Value Theorem and the Mean Value Theorem to prove that the equation cos...

Use the Intermediate Value Theorem and the Mean Value Theorem to prove that the equation cos (x) = -10x has exactly one real root. Not permitted to use words like "Nope", "Why?", or "aerkewmwrt". Will be glad if you can help me with this question, will like to add some of your points to the one I have already summed up.. Thanks

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and such that f(a)=f(b). Then there exists at least one point c on (a,b) such that f'(c)=0." Rolle's Theorem requires three conditions be satisified. (a) What are these three conditions? (b) Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow, i.e., there is no point c in (a,b) such that f'(c)=0. Each...

State and prove the Generalised Mean Value Theorem.

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Check the hypotheses of Rolle's Theorem and the mean value theorem and find a value of...

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Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then...

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