Question 1

Let f(x,y) = 2x2+ y2 - 7x - 8y +9. (A) Find the minimum value of f(x,y) when y = 1. (B) Explain why the answer to part (A) is not the minimum value of the function f(x,y). (A) The minimum value of f(x, 1) is (Simplify your answer.) (B) The answer to part (A) is not the minimum value of the function f(x,y) because the minimum value of for example, is , which is less than the answer to part (A). (Simplify your answer.) f(x, - 1), f(0,y), f(x, 0),Find f'(x) if f(x) = 7x"+ e 3x f'(X) =Use Lagrange multipliers Minimize the product of two numbers if their difference must be 12. The minimum product of two numbers whose difference is 12 is (Simplify your answer.)