Q18Comprehension1 Mark31 Aug 2025
Passage
Based on the above data, answer the given subquestions. Consider a metallic plate which occupies the space D bounded between the curves y = -x^2 + 1 and the x-axis as shown (the shaded region) in the figure. The temperature at any point on the metallic plate is given by the function T: D -> R defined by T(x, y) = 10 + xy + x^3 - x/3, for all in D. The following notation will be used in the subquestions that follow. - The interior of D: Int(D) = { in D | y < -x^2 + 1 and y > 0 }. - The boundary components of D: gamma_1 = { in D | y = -x^2 + 1, x in } gamma_2 = { | x in } - The corners of D: v_1=(-1, 0), v_2 =
Let v_1 and v_2 denote the one-variable functions obtained by restricting T on gamma_1 and gamma_2, respectively, i.e., v_1(x) = T(x, -x^2 + 1), v_2(x) = T(x, 0), for x in . Which of the following statements is true?