Consider the problem minimise f(x1, x2, x3) = x² + x²x² + 2x1x2 + x² +8x2 subject to 2x1 + 5x₂ + x3 = 3. (a) Use the reduced gradient to determine which of the following are stationary points: (i) (0, 0, 2); (ii) (0,0,3); (iii) (1,0,1). (b) For each staionary point you found in part (a), use the reduce Hessian to deter- mine whether they are a local minima, a local maxima or a local saddle.

Q: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

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A: It is given that fx and gx two distinct function.

Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

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Q: If f(x) = 2 + 3x – 4x², determine the value of the dependent variable f(5) – f(3). Show your work.

A: We can solve the problem by putting the value 5 and 3 in the given function.

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