find the critical points of the function fourth root x^5 *(x-4)^2.

Answer 1

f(x) = x^5/4(x - 4)²

f'(x) = (5/4)x^1/4(x - 4)² + x^5/4(2)(x - 4) = x^1/4(x - 4)[(5/4)(x - 4) + 2x] = x^1/4(x - 4)[(5/4)x - 5 + 2x]

f'(x) = x^1/4(x -4)[(13/4)x - 5] = 0 when x = 0, 4, 20/13

f has critical points when x = 0, 4, 20/13