qns 7,8,9....left 6 and 10...

7a)using product rule to find dy/dx will give you 5(x-2)^3(x-2/5),so when dy/dx=0,x=2 or x=2/5.As x increase through 2/5, dy/dx change from positive to negative.so,2/5 is the max point.As x increase through 2,dy/dx change from negative to positive,so 2 is the min point.

7b)using product rule,to find dy/dx will give you 4(x-3)^2)(x-3/4), so when dy/dx=0 x=3 or x=3/4. As x increases through 3/4...dy/dx change from negative to positive, therefore it is the min point.As x increase through 3 dy/dx > or equal to o,hence 3 is the stationery point of inflexion.

8)dy/dx(x^2-4x+6)=2x-4
2x=4,x=2.subx=2, into(x^2-4x+6),y=2
a=(2,2).As x increases through 2,dy/dx changes from negative to positive, so it is the minimum point.

9a)dy/dx(2x^3-9x^2+12x-4)=6x^2-18x+12
=6(x-1)(x-2) (shown)

9b)dy/dx=0,when x=1,y=1. when x=2,y=0

9c)As x increases through 1,dy/dx changes from positive to negative,so (1,1)is the max point.
As x increases through 2,dy/dx changes from negative to positive,so(2,0)is the min point


Legend:max point=maximum point, min point=minimum point ..hope this will help u all in the homework