Page 62 - Math SL HB Sem 2

(f) For 0 < /< n,

(D sketch the graph of ft';

(il) find the time at which the height is changing most rapidly.
(s)
(Total 22 marks)

6. consider the function/(:) 6@-r) 1 ,x * I
tp,-1;L) ",

<
(a) Sketch the curve of ffor -2 x <2, including any asymptotes.
(3)

(b) (i) Write down the equation of the vertical asymptote off

(iD Write down which one ofthe following expressions does not represent an area
between the curve of/and the.x-axis.

(r)d'
!; "f

t: f(x)dx

(iii) Justifu your answer.
(3)

:
(c) The region between the curve and the.r-axis between .x = I and .x 1.5 is rotated through
360o about the.r-axis. Let I/ be the volume formed.

(D Write down an expression to represent /.

(iD Hence write down the value of Z.
(4)

(d) Find/' (x).
(4)

(") (i) Write down the value of -x at the minimum point on the curve off

:
(iD The equation/(x) k has no solutions forp ( ,t < q. Write down the value ofp and
of q.
(3)
(Total l7 marks)

6