The plane tangent to the surface z fxy at 234 has eq z 4x2

Solution

sol f(-2+h,3+k)= f(-2,3)+hdf/dx+kdf/dy approximately, where the ds are partial, calculated at (-2,3) h=-0.1, k=0.1 The tangent plane has equation z-4=(df/dx)(x+2)+(df/dy)(y-3) which is identical to 4x+2y+z=2 from which you get df/dx (calculated at (-2,3) to be -4 and df/dy to be -2. Using the first line you can obtain an estimate of f(-2.1, 3.1)