f(x,y)=2x2−e2x−3y−8 (-1,2)
Definition:
Let S be a surface defined by a differentiable function z = f(x, y), and let Po=(xo,yo) be a point in the domain of f. Then, the equation of the tangent plane to S at Po is given by
z=f(xo,yo)+fx(xo−yo)+fy(xo,yo)(y−yo) 1-equation
First, we must calculate fx(x,y) and fy(x,y), the we use 1-equation with x0=−1 and
yo=2
fx(x,y)=4x−2e2x
fy(x,y)=−3
f(−1,2)=2(−1)2−e2∗(−1)−3∗2−8=−11−e21
fx(−1,2)=4∗(−1)−2e2∗(−1)=−4−e22
fy(−1,2)=−3
Then 1-equation becomes
z = −11−e21 + (−4−e22)(x+1) + (−3)(y+3)
z=−11−e21−4x−e22x−4−e21−3y−9
z = −4x−e22x−3y−e21−24
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