How do you find critical point for this equation #f(x,y)=6x^7+7y^2+8xy+9#?

Answer 1

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Answer 2

To find critical points for the equation ( f(x,y) = 6x^7 + 7y^2 + 8xy + 9 ), we need to compute the partial derivatives of the function with respect to ( x ) and ( y ), and then solve the system of equations formed by setting these partial derivatives equal to zero. The critical points occur at the solutions to this system.

Compute the partial derivative of ( f ) with respect to ( x ):

( \frac{\partial f}{\partial x} = 42x^6 + 8y )
Compute the partial derivative of ( f ) with respect to ( y ):

( \frac{\partial f}{\partial y} = 14y + 8x )
Set both partial derivatives equal to zero and solve the resulting system of equations:

( 42x^6 + 8y = 0 )

( 14y + 8x = 0 )
Solve the system of equations for ( x ) and ( y ). These solutions represent the critical points of the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.