Understanding Engineering Mathematics

(iii) Point of inflection at (0, 0)

(iv) Min at (5, 2), max at (−5,−2)

(v) Min at (3, 23), max at (2, 24), point of inflection atx=^52

(vi) Min atx=^32 ,minatx=−2, point of inflection atx=−^14

B. Max of

16

3

√

3

atx=−

2

√

3

and min of−

16

3

√

3

atx=

2

√

3

. The slope at the point of

inflection,x=0, is−4.

10.3.4 Curve sketching in Cartesian coordinates

y

y

y

y

x x x

y y

y

− 1 1 2 x − 1 x x x

1

− 1

1

1

0

1

1

0 0 0

4

0 0 0

(i) (ii) (iii) (iv)

(v) (vi) (vii)

10.3.5 Applications of integration – area under a curve

A.(i)

28

3

(ii)

3

2

−ln 2

(iii) e (iv)

1

2

(v)

28

3

(vi)

π

4

B.(i)− 4 (ii) 0

C. 1

D.

11

6