100年 - 100 國立政治大學轉學生招生考試_應用數學系：微積分(一)#122269

科目：研究所、轉學考(插大)-微積分 | 年份：100年 | 選擇題數：0 | 申論題數：9

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (9)

10% (a)66c6963f590fd.jpg = 4.

10% (b) 66c69658e044e.jpg= 0.
10% (a) Show that if f'(a) = 0 and f''(a) ＜ 0, then f(a) is a relative maximum.
10% (b) Show that if f'(a) = 0 and f''(a) ＞ 0, then f(a) is a relative minimum.
10% (a) Find f'(x).
10% (b) Find an equation of the tangent line of f(x) at x=2.

10% (a) Show that if f(a, b) is optimal, then66c696c0b451f.jpg
10% (b) Show that fx(a,b) + λgx(a,b) = fy(a,b) + λgy(a,b) where λ is a Lagrange multiplier.
5. (20%) Let z = f(x,y) be a function and fx and fy exist and z= P(x,y) be the tangent plane of z = f(x,y) at (a, b, f(a,b)). Show that P(a+Δx, b+Δy) - P(a, b) = fx(a,b)Δx+fy(a,b)Δy where Δx is the change in x and Δy is the change in y.