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Find the absolute extrema of the function f(x, y) = (4x - x^2) \cos y on the rectangular plate...

Question:

Find the absolute extrema of the function {eq}f(x, y) = (4x - x^2) \cos y {/eq} on the rectangular plate {eq}1 \leq x \leq 3, -\pi/4 \leq y \leq \pi/4 {/eq} .

Finding Extrema For A Function:

For a given function the extrema value is at the point when the function will be minimum. To Find this value first we need to differentiate the function and equate it to zero and then we need to find the whether the condition is being satisfied or not that is given in the problem.

Answer and Explanation:

Given function

{eq}f(x,y)=(4x-x^2)cos y {/eq}

Equating the equation to zero after differentiation.

(4-2x)cos y =0

Either cos y = 0 or 4-2x = 0

x...

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