Q19Comprehension2 Marks31 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 =
Comparing the critical points on the interior, the boundary components, and the corners, find the temperature at the hottest point on the metallic plate.
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