Question

Find the critical numbers of the function f(x) = x^6(x − 1)^5

Answer 1

... requires implicit differentiation...

Answer 2

Given function f(x) = x^6(x − 1)^5
Take the derivative:
f'(x) = 6x^5(x - 1)^5 + 5x^6(x - 1)^4
Set the derivative equal to 0 and solve:
6x^5(x - 1)^5 + 5x^6(x - 1)^4 = 0
(x^5(x - 1)^4) [6(x - 1) + 5x] = 0
(x^5(x - 1)^4) (x - 6) = 0
x = 0 and x = 1 and x = 6
Hence these are the critical points of the function

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