Everything Maths Grade 12

CHAPTER 7. DIFFERENTIAL CALCULUS 7.5

Step 5 : Determine the y-coordinates of the turning points by substituting the x values

obtained in the previous step, into the expression for f (x).

y coordinate of turning point is given by calculating g(^12 ).

g

�

1

2

�

=

�

1

2

� 2

−

�

1

2

�

+ 2

=

1

4

−

1

2

+ 2

=

7

4

The turning point is at (^12 ;^74 )

Step 6 : Draw a neat sketch

1

2

3

4

5

6

7

8

9

3 2 − − 1 − 1 2 3 4

y

x

�

�

( 0 , 5 ; 1 , 75 )

Example 12: Sketching Graphs

QUESTION

Sketch the graph of g(x) =−x^3 + 6x^2 − 9 x + 4.

SOLUTION

Step 1 : Determine the shape of the graph

The leading coefficientof x is < 0 therefore the graph isa parabola with a

maximum.