Compute the gradient of the following functions and evaluate it at the given point P. g(x,y)=x2−4x2y−8xy2;P(−1,2)

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Compute the gradient of the following functions and evaluate it at the given point P.  g(x,y)=x2−4x2y−8xy2;P(−1,2)

berggansS · Accepted Answer

Step 1  The function is given as, g(x,y)=x2−4x2y−8xy2  To find the gradient of the given function at (−1 , 2).  The gradient is just the  vector of partial derivatives, the partial derivatives will be as,  ∂g∂x=2x−8xy−8y2 and  ∂g∂y=−4x2−16xy  At point (−1,2),  ∂g∂x=2(−1)−8(−1)(2)−8(2)2  =-2+16-32  =-18  Step 2  and  ∂g∂y=−4(−12)−16(−1)(2)  =-4+32  =28  Since, the gradient is represented in vector form as, ∂g∂xi+∂g∂yj,  gradient =∂g∂xi+∂g∂yj  =-18i+28j  Hence, the gradient for the given function is −18i+28j.

Compute the gradient of the following functions and evaluate it

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