A student was asked to find the equation of the tangent plane to the surface z = x² - y² at the point (x, y) = (4, 5). The student's answer was z = 4x³ (x-4)- 2y(y-5)+231. (a) At a glance, how do you know this is wrong? This answer is wrong because the constant. equation of the tangent plane is always (b) What mistake did the student make? The partial derivatives used in the formula of the tangent plane are incorrect. (c) Answer the question correctly. The equation of the plane is 256(x-4)- 10(y-5)-1(2) Col ag because the gent plane is always he student make? tives used in the form ne are incorrect. n correctly. e plane is 256(x-4) **O" constant. Choose one constant. cubic. 6 quadratic. linear. quartic. Tory of -/3 E 1 (z) a) Choose one The student substituted the incorrect values x = -4 b) and y = -5 into the formula of a tangent plane. The student did not simplify the formula of the tangent plane. (c) The partial derivatives used in the formula of the tangent plane are incorrect. The student did not substitute the values of x = 4 and y = 5 into the formula for z used in the formula of a tangent plane. The student did not substitute the values x = 4 and y = 5 into the formulas for the partial derivatives used in the formula of a tangent plane. 5715