Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables f(x) = x1 + x₁x₂ + (1+x₂)². Evaluate these derivatives at x = 0 and show that G(0) is not positive definite. Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x2 - 4x₁ - 8x2 b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x² d. f(x) = 2x²-3x² - 6x₁x₂(x₂-x₁ - 1) e. f(x) = (x₂-x²)² - x²

Q: Find the derivative of f(w)=w78+2w.

A: dxndx= nxn-1---- Formula f(w) = w78 + 2w f'(w) = d(w78+2w)dw = 78 w77 + 2

Q: Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables…

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Q: У y = |1 - х - 1+х

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Q: Q. No. 2: Solve the following partial differential equations (a) (Dz + D,Dy – 6D,²)u = ycosx 2

A: From the given information. The partial differential equation is as follows. Dx2+DxDy-6Dy2u=ycosx

Q: R(w) = w? 8w + 20

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