Question

How many critical points does the function `f(x) = (x+2)^5 (x^2-1)^4` have?

Answer 1

5 critical points 1, -1, -2 , `(-8+-sqrt129)/13`

Find f'(x) = `5(x+2)^4 (x^2-1)^4 + (x+2)^5 4(x^2-1)^3 2x`

= `(x+2)^4 (x^2 -1)^3( 5x^2 -5 +8x^2+16x)`

=`(x+2)^4 (x^2 -1)^3( 13x^2 +16x -5)`

Critical points would be that make f '(x) =0

These would be x=1,-1, -2,`(-8+-sqrt129)/13`