5.6 Stationary pointsIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 5.6 Stationary points

1. The function $f$ is given by $f(x)=2x^3-9x^2+12x$.
   Justify that the point where $x=1$ is a local maximum, and write down its coordinates.2 marks
2. The gradient function of a curve $y=f(x)$ is $f'(x)=(x-1)(x+3)$.
   Justify that $f$ has a local minimum at $x=1$.2 marks
3. A company sells $x$ hundred units of a product each week, where $0\le x\le 8$. The weekly profit, $P$ thousand USD, is modelled by $P(x)=-x^3+9x^2-15x+10$.
   Find $P'(x)$ and hence find the values of $x$ for which $P'(x)=0$.3 marks