42L T 6. Given that V - Use partial derivative to approximate the K2 maximum percentage...

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42L T 6. Given that V - Use partial derivative to approximate the K2 maximum percentage error in estimating V, if the error in estimating K, if the error in measuring L and V are 4% and 1%. [6 marks] 7. Find all critical points of f (x, y) = 2x3 + 6xy2-3y3-150x and classify each critical point as a local maximum, local minimum or a saddle point by using partial derivatives. [9 marks] Differentiations Differentiations of Inverse Functions d d = 0, k constant. 1 = <1... da 1-2 d d -1 =na"-1 -1 [cosx] = |x| < 1. dr d M-2. d [tanr] = 1+x21 d d [cot 1] -1 1+21 d d 1 dax [cos.x]=-sin.r. [sec x] = |x|> 1. dax d d dr [sin x] = cos r. [cosec]= == -1 x>1. d d [tanr] = sec r. d.c d.c - sinh 1 1 x] = Va2+1 d [cot x] = -cosecx. d dr dr d [secr] = sec. tan r. d -1 da 1 -1 [cosh'] = 1'>1. - tanh 'r = 1 21 || <1. d d dr [cosec.x] =-coseca cota. -1 [cothx] = || 1. 1 1-2 d d [cosh r] = sinh.r. dr dr sech-z]= 1 0 42L T 6. Given that V - Use partial derivative to approximate the K2 maximum percentage error in estimating V, if the error in estimating K, if the error in measuring L and V are 4% and 1%. [6 marks] 7. Find all critical points of f (x, y) = 2x3 + 6xy2-3y3-150x and classify each critical point as a local maximum, local minimum or a saddle point by using partial derivatives. [9 marks] Differentiations Differentiations of Inverse Functions d d = 0, k constant. 1 = <1... da 1-2 d d -1 =na"-1 -1 [cosx] = |x| < 1. dr d M-2. d [tanr] = 1+x21 d d [cot 1] -1 1+21 d d 1 dax [cos.x]=-sin.r. [sec x] = |x|> 1. dax d d dr [sin x] = cos r. [cosec]= == -1 x>1. d d [tanr] = sec r. d.c d.c - sinh 1 1 x] = Va2+1 d [cot x] = -cosecx. d dr dr d [secr] = sec. tan r. d -1 da 1 -1 [cosh'] = 1'>1. - tanh 'r = 1 21 || <1. d d dr [cosec.x] =-coseca cota. -1 [cothx] = || 1. 1 1-2 d d [cosh r] = sinh.r. dr dr sech-z]= 1 0