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 The temperature g (t) at time t of a given point of a heated iron rod is given by

g (t) = ,           where t > 0.

(a)     Find the interval where g¢ (t) > 0.

(4)

(b)     Find the interval where g² (t) > 0 and the interval where g² (t) < 0.

(5)

(c)     Find the value of t where the graph of g (t) has a point of inflexion.

(3)

(d)     Let t* be a value of t for which g¢ (t*) = 0 and g² (t*) < 0. Find t*.

(3)

(e)     Find the point where the normal to the graph of g (t) at the point
(t*, g (t*)) meets the t-axis.

(3)

(Total 18 marks)