We know that, . If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I Given ,f(x)=x3−6x2+9x+10 Differentiating, we get f′(x)=3x2−12x+9 f(x) is increasing function ⇒f′(x)≥0 ⇒3x2−12x+9≥0 ⇒x2−4x+3≥0. ⇒(x−3)(x−1)≥0 Hence, x∈(−∞,1]∪[3,∞) The interval in which the function f(x)=x3−6x2+9x+10 is increasing in (−∞,1]∪[3,∞)