x^8(x-2)^7 find the critical numbers

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function f(x) = x^8*(x - 2)^7.

The critical numbers of a function are those where f'(x) = 0 or f'(x) is undefined.

For f(x) = x^8*(x - 2)^7

f'(x) = 8*x^7*(x - 2)^7 + x^8*7*(x - 2)^7

8*x^7*(x - 2)^7 + x^8*7*(x - 2)^6

=> (x^7*(x - 2)^6)(8(x - 2) + 7x)

=> (x^7*(x - 2)^6)(8x - 16 + 7x)

=> (x^7*(x - 2)^6)(15x - 16)

(x^7*(x - 2)^6)(15x - 16) = 0

=> x = 0, x = 2 and x = 16/15

The critical numbers are x = 0, x = 2 and x = 16/15

We’ve answered 318,928 questions. We can answer yours, too.

Ask a question