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Question 7 (a) Verify by differentiation that

`\int (x)/(2\sqrt(2+x))dx=(1)/(3)(x-4)\sqrt(2+x)+K`

where

`K`

is a constant. [6 marks] (b) Consider the function

`f(x)=x^(3)-3x^(2)`

. (i) Determine the critical number(s) of

`f`

. [2 marks] (ii) Find the intervals where

`f`

is increasing. [3 marks] (iii) Find the intervals where

`f`

is decreasing. [3 marks] (iv) Find the local extrema of

`f`

. [2 marks] (v) Sketch the graph of

`f`

, clearly indicating the intercepts. [5 marks] (c) Use L'Hôpital's rule to evaluate

`\lim_(x->3)((1)/(x)-(1)/(3))/(x^(2)-9)`

[4 marks]