Chapter(^5)
P1^
(ii) At (1, 0), ddyx = − 1
At (2, 0), d
d
y
x
= 1
(iii) At (1, 0),
tangent is y = −x + 1,
normal is y = x − 1
At (2, 0),
tangent is y = x − 2,
normal is y = −x + 2
(iv) A square
9 (i) (1, −7) and (4, −4)
(ii) (^) ddyx = 4 x − 9. At (1, −7),
tangent is y = − 5 x − 2;
at (4, −4), tangent is
y = 7 x − 32.
(iii) (2.5, −14.5)
(iv) No
10 (i) y = 12 x + (^12)
(ii) y = 3 − 2 x
(iii) 212 units
11 (i) y = − 14 x + 1
(ii) y = 4 x − (^712)
(iii) 812 square units
12 (i) 1
2 x
(ii) (^) () 161 ,−^34
(iii) No. Point () 161 ,− 43 does not
lie on the line y = 2 x − 1.
13 (i) y = 5 x −^74
(ii) 20 y + 4 x + 9 = 0
(iii) 1320 square units
14 27.4 units
15 (i) 2 y = x + 6
(ii) 9 square units
16 (i) 3 +^23
x
(ii) 5
(iii) y = 5 x − 3
17 (i) 2 x − (^12)
x
(ii) 1
(iv) (–2.4, 5.4), (0.4, 2.6)
18 2623 units
19 (i) (a) x = 1^12 and x = 3
(b) y = 2x – 2
(c) 36.9°
(ii) k 3.875
20 (ii) (–8, 6)
(iii) 11.2 units
Activity 5.6 (Page 146)
(i) 3
(ii) 0
(iii) (0, 0) maximum; minima to left
and right of this.
(iv) No
(v) No
(vi) About −2.5
Exercise 5E (Page 151)
1 (i) (^) ddyx = 2 x + 8;
(^) ddyx = 0 when x = − 4
(ii) Minimum
(iv)
2 (i) (^) ddyx = 2 x + 5;
(^) ddyx = 0 when x=–2^12
(ii) Minimum
(iii) (^) y=–4^14
(iv)
3 (i) (^) ddyx = 3 x^2 − 12;
(^) ddyx = 0 when x = −2 or 2
(ii) Minimum at x = 2,
maximum at x = − 2
(iii) When x = −2, y = 18;
when x = 2, y = − 14
(iv)
4 (i) A maximum at (0, 0),
a minimum at (4, −32)
(ii)
5 ddyx = 3 x^2 − 1
6 (i) (^) ddyx = 3 x^2 + 4
O
–1 1 2
–5
5
10
15
x
y
x
y
O
–3
–4
13
x
y
2
–4–^14
–2^1 – 2 O
x
y
2
–
–2 O 2
x
y
O
–32