Basic statistics for finance
tutorial 5
Q1) The derivatives are (a) (i) 8x3 , −6x−3 , (ii) 24x3 e3x , (iii) 4x . (b) (i)
−10(2x − 7)−6 , (ii) 3x2 + 4x − 23, (iii) 1.
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Q2) (a) The second derivatives are (i) 24x2 , (ii) 72x2 (1 + 4x4 )e3x . (b) We
have zx = 2x + 4y, zy = 4x + 4y, zxx = 2, zyy = 4, and zxy = 4.
Q3) (i) −24, (ii) local maximum at x = −1 and local minimum as x = 3.
Q4) (i) We have zx = −4x + 12 + 2y, zy = 2x − 2y − 4, zxx = −4, zyy = −2, and zxy
= 2. (ii) local maximum at x = 4, y = 2. (iii) local maximum at x = y = 4.