Find the critical numbers of the function f(x) = x^6*(x - 2)^5.

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function f(x) = x^6*(x - 2)^5. The critical numbers of the function lie at the solution of the equation f'(x) = 0

f'(x) = 6x^5*(x - 2)^5 + x^6*5*(x - 2)^4

f'(x) = 0

=> 6x^5*(x - 2)^5 + x^6*5*(x - 2)^4 = 0

=> x^5*(x - 2)^4*(6x - 12 + 5x) = 0

=> x^5*(x - 2)^4*(11x - 12) = 0

=> x = 0, x = 2 and x = 12/11

The critical points of f(x) lie at x = 0, x = 12/11 and x = 2

Here is a general video on finding critical numbers:

We’ve answered 318,979 questions. We can answer yours, too.

Ask a question