Page 28 - Math SL HB Sem 2

@ Let/(x) = 3 cos 2x * sin2 x.

(a) Show that/'(r) = -5 sin 2r.

L L :
(b) In the interval , one normal to the graph of/has equation r t.
44
=ra
Find the value ofk.
(Total 6 marks)

,,'\
f
a, Consider the funct iton ($: 4l + 2x. Find the equation ofthe normal to the curve of/at the
Point where =l '
'r
(rotrr 6 marks)

e Differentiate each ofthe following with respect to x.

(a) y: sin 3*
(1)

(b) y: xtanx
(2\

ln.r
(c)
x
(3)
(Total 6 marks)

7. On the axes below, sketch a curve y=f(x) which satisfies the following conditions.

f(x) f'(x) f" (x)
.lr
-23x<0 negative positive

0 I 0 positive

0<x<l positive positive

I 2 positive 0

| <x32 positive negative

4