Answer to Question #320437 in Real Analysis for Olatunde

Question

Separate the interval in which the function f defined on R by f(x)=2x3-15x2+36x+5 for all x∈R is increasing

Answer 1

$f(x)$ is increasing on the interval in which $f’(x)>0$

$f’(x)=6x^2-30x+36>0$

$x^2-5x+6>0$

$(x-2)(x-3)>0$

$x\in(-\infin;2)\cup(3;\infty).$

Answer: f(x) is increasing on the interval $x\in(-\infin;2)\cup(3;\infty).$