Find the interval on which the following function is decreasing f(x)=(x^2/2)+5x-6ln(x).

Question

Find the interval on which the following function is decreasing f(x)=(x^2/2)+5x-6ln(x).

Answer 1

f(x) = x²/2 + 5x - 6lnx; domain f(x): x > 0.

f'(x) = x + 5 - 6/x; f'(x) < 0 for f(x) to be increasing; x + 5 - 6/x < 0; because x > 0 we have x² + 5x - 6 < 0;

(x + 6)(x -1) < 0 so - 6 < x < 1 but x > 0. So f(x) decreasing if 0< x < 1.

Answer: (0, 1)