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

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Answer 1 · 2015-04-16T08:20:40

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, $(-8+-sqrt129)/13$

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