The equation for a plane tangent to z = f(x, y) at a point (To, yo) is given by 2 = = f(xo, yo) + fz(xo, Yo) (x − xo) + fy(xo, yo)(y - Yo) If we wanted to find an equation for the plane tangent to f(x, y) we'd start by calculating these: f(xo, yo) = 159 fz(xo, Yo) = fy(xo, yo) = 9xy 3y + 7x² at the point (3, 4), Consider the function described by the table below. y 3 4 X 1 -2 -5 -10 -17 -26 2 -14 -17 -22 -29 -38 -34 -37 -42 -49 -58 -62 -65 -70 -77 -86 5 -98-101 -106 -113-122 At the point (4, 2), A) f(4, 2) = -65 B) Estimate the partial derivatives by averaging the slopes on either side of the point. For example, if you wanted to estimate fat (10, 12) you'd find the slope from f(9, 12) to f(10, 12), and the slope from f(10, 12) to f(11, 12), and average the two slopes. fz(4, 2)~ fy(4, 2)~ C) Use linear approximation based on the values above to estimate f(4.1, 2.4) f(4.1, 2.4)~ N→ 345