Sketch the curve y=x(x-2)^3 showing any stationary points and points of inflection

Step-by-step explanation:

hello :

let   :   y=f(x)

f(x)==x(x-2)^3   so : f'(x) = 1.(x-2)^3+3x(x-2)²

f'(x) = (x-2)²(x-2+3x)

f'(x) = (x-2)²(4x-2)

f'(x) =0    : x=2  or x=1/2

the minumum is (1/2 ,f(2))

the inflection points use f"(x) = 0continu

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)