5.2 Increasing and decreasing functionsIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 5.2 Increasing and decreasing functions

1. A function $f$ has derivative $f'(x)=x^2+x-6$.
   Find the set of values of $x$ for which $f$ is increasing.2 marks
2. A continuous function $g$ is defined for $-4\le x\le 6$. Its derivative satisfies $g'(x)>0$ for $-4<x<-1$, $g'(x)=0$ at $x=-1$ and at $x=3$, $g'(x)<0$ for $-1<x<3$, and $g'(x)>0$ for $3<x<6$.
   Given that $g(-1)=7$, explain why $g(2)<7$.2 marks
3. The height, $h$ metres, of a drone $t$ seconds after take-off is modelled by $h(t)=t^3-12t^2+36t+5$, for $0\le t\le 8$.
   Find $h'(t)$. Hence use your GDC to find the values of $t$ for which $h'(t)=0$.3 marks