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Math  /  Algebra

QuestionFor the function, evaluate the given expression. f(x,y)=xey−yex, find f(4,−4)f(4,−4)=\begin{array}{l} f(x, y)=x e^{y}-y e^{x}, \text { find } f(4,-4) \\ f(4,-4)= \end{array}

Studdy Solution

STEP 1

1. We are given the function f(x,y)=xey−yex f(x, y) = x e^{y} - y e^{x} .
2. We need to evaluate the function at the point (4,−4) (4, -4) .

STEP 2

1. Substitute x=4 x = 4 and y=−4 y = -4 into the function.
2. Simplify the expression to find f(4,−4) f(4, -4) .

STEP 3

Substitute x=4 x = 4 and y=−4 y = -4 into f(x,y) f(x, y) :
f(4,−4)=4e−4−(−4)e4 f(4, -4) = 4 e^{-4} - (-4) e^{4}

STEP 4

Simplify the expression:
f(4,−4)=4e−4+4e4 f(4, -4) = 4 e^{-4} + 4 e^{4}

STEP 5

Factor out the common factor of 4 4 :
f(4,−4)=4(e−4+e4) f(4, -4) = 4 (e^{-4} + e^{4})
The value of f(4,−4) f(4, -4) is:
4(e−4+e4) \boxed{4 (e^{-4} + e^{4})}

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