The diagram shows a sketch of the graph with equation f(x) = 6x 2x. There is

The diagram shows a sketch of the graph with equation f(x) = 6x² − 2x³. There is a minimum at the origin, a maximum at the point A(2, 8) and it cuts the x-axis at B(3, 0).

a) On separate diagrams, sketch the graphs with equations

i) y = f(2x)

ii) y = f(x + 1).

On each sketch, show where the curve cuts the x-axis and mark the coordinates of A and B.

b) The curve with equation y = f(x) + c has a maximum point at (2, 3). State the value of c.

c) The curve with equation y = df(x + e) has
a maximum point at (4, 4).
State the value of d and the value of e.

Transcribed Image Text:

0 A(2,8) B(3,0) X