help with some differentiate problems (1 Viewer)

[wolf7]

find any stationary points on the curve

y=(4x^2-1)^4

and determine their nature

also

the curve y = ax^3 +bx^2 - x +5 has a point of inflexion at (1,-2)

find the values of a and b

 

[klaw]

y'=32x(4x^2-1)^3=32x[(2x+1)(2x-1)]^3
When y'=0, x=0 or +-1/2
When x=0, y=1
When x=1/2, y=0
When x=-1/2, y=0
Then just use product rule to find y'' and sub the x values in to determine their nature.

 

[klaw]

y=ax^3+bx^2-x+5
y'=3ax^2+2bx-1
y''=6ax+2b

When x=1, y=-2
.:-2=a+b-1+5
.:a+b=-6

When x=1, y''=0
.:6a+2b=0

Then solve simultaneously

 

[wolf7]

thanx, i get the question now