Finding the second derivative of the given vector function r(t) = 3t 4 1- 31 2 + 4t k.
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- 12 help use variation of parameters to finda general solution to the differntial equation given the function y1 and y2 are linearly independent solutions to the corresponding homogenous equation for t>0find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. 1. ƒ(x) = x2 + 2x, a = 0.1 2. ƒ(x) = x-1, a = 0.9 3. ƒ(x) = 2x2 + 3x - 3, a = -0.9 4. ƒ(x) = 1 + x, a = 8.11. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example
- find a linearization at a suitably chosen integernear a at which the given function and its derivative are easy to evaluate. ƒ(x) = 2x2 + 3x - 3, a = -0.9Find the critical numbers of f(x) = x4(x-1)3 A. What does the second derivative test tell you about the behavior of f at these critical numbers? B. What does the first derivative test tell you?f:[0,1] -> [0,1] such that f(x)=x^2 has two fixed points. Is this true?
- Find the critical point of the function f(x,y)=6x−2y^2−ln(|x+y|). c=Use the Second Derivative Test to determine whether it isA. a saddle pointB. a local maximumC. test failsD. a local minimumFind a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x)=2x2+5x-3, a=-0.9Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)).c = Use the Second Derivative Test to determine whether it is• A. a local maximum• B. a saddle point• C. a local minimum• D. test fails
- What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx - x2fxx1. Use the Cauchy-Riemann equation to determine if the function f(z) = x3 - i(2 - y)3 is analytic or not. Provide all the sufficient conditions and the domain of analyticity and then find the derivative if it exists.