4. (i) Let f R2 R be defined by f(x1, x2) = 2x8x1x2+4x+1. Find all local minima of f on R². [20 Marks] (ii) Does have a global minimum on R²? [10 Marks]

Determine if the statement is true or false. If the statement is false, then correct it and make it true. All functions have a local maximum value and a local minimum value.

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

A company that makes and sells baseball caps has found that the total monthly cost C in dollars of producing x caps is given by the function C(x)=0.2x280x+9000. Find the production level that will minimize the monthly cost and find the minimum cost.