A student was asked to find the equation of the tangent plane to the surface z=x^3-y^2 at the point (x,y)=(2,3). The student’s answer was z= 3x^2(x-2)-2y(y-3)-1.
a)At a glance, how do you know this is wrong?
b)What mistake did the student make?
c)Answer the question correctly.
calculus III
2008-02-27 9:45 pm
回答 (2)
2008-03-04 1:19 pm
✔ 最佳答案
a) the answer is a quadratic equation, but the equation of a plane should be a linear equationb) the student didn't plug (xo,yo) = (2,3) into the partial derivatives
c) z+1 = 12(x-2) - 6(y-3)
參考: my tutoring experience and Stewart 5th edition textbook
2008-03-04 1:06 pm
a> it does not match the plane equation
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