Chem452 HW

# Chem452 HW - Chem 452 HW I(A Winter 2011 ANSWERS for CHEM...

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Chem 452 – HW I(A) Winter 2011 ANSWERS for CHEM 452 HW 1(A) 1 2 9 x f(x) = cx n , df / dx = ncx n-1 , where c is a constant 2 ( ) 4/3 1/3 1 3 x x a x a y = a x+y and f(x) = cx n , df / dx = ncx n-1 (c is a constant) 3 3ln( ) 3 x + ( ) ln( ), 1/ f x x df dx x = = and d / dx (g(x)·h(x)) = ( d / dx g(x))(h(x)) + (g(x))( d / dx h(x)) 4 2 10 (1 ) x xe x + ( ) , ax ax f x e df dx ae = = (where a is a constant) and d / dx (g(x)·h(x)) = ( d / dx g(x))(h(x)) + (g(x))( d / dx h(x)) 5 2 1 1 x ( ) 2 ( ) ( ) '( ) ( ) '( ) ( ) ( ) g x h x g x g x h x h x h x = (Quotient Rule) 6 1 x = (local min) 1/3 x = − (local max) x = b ± b 2 4 ac 2 a Local min occurs at df / dx = 0 and d 2 f / dx 2 > 0 Local max occurs at df / dx = 0 and d 2 f / dx 2 < 0 7 12 [ ] 2 3 4 4 3 3 1 8 1 12 x x =− = + = ax n dx = 1 n + 1 ( ) ax n + 1 for n 1 8 2 1 nRTln z z [ ] ( ) 2 2 1 1 2 1 ln
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