A first order nonlinear system is described by the equation ẋ = −f(x) where f(x) is a continuous and differentiable nonlinear function that satisfies the following: f(0) = 0; f(x) > 0 for x > 0; f(x) < 0 for x < 0. Use the Lyapunov function V(x) = x2 /2 to show that the system is stable near the origin.

Q: f(x) = x2 -x-7 is The relative maximum value of and its relative minimum value is

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Q: Determine the maximum or minimum value for y = −2(x − 7)(x − 5) and state the value of x for which…

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Q: Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

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Q: Find values of m and b such that: f(x)=x2+1          if x=1 is differentiable.

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Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

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Q: Function f(x) = x4 - 12x3 + 46x2 - 60x + 30 has critical points at:I. x = 1; II. x = 3; III. x = 6.…

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Q: What do you mean by asymptotically stable for autonomous equations ?

A: Given: asymptotically stale for autonomous equation A critical point x∘ of an autonomous system is…