IB Maths AI SL AI 5.1 practice question

Paper 1Easy6 marks

A bakery models its weekly profit, $P$ in thousands of dollars, when it produces $q$ hundreds of loaves per week, by

P(q)=q^3-6q^2+9q+2,\qquad 0\leq q\leq 4.

Figure 1 shows the graph of this model.

(a)

Use a GDC to generate $P'(q)$ then solve $P'(q)=0$ Give your answers to three significant figures.

[3]

(b)

Use Figure 1 to write down the coordinates of the local maximum point and the local minimum point.

[2]

(c)

Interpret the local maximum point in the context of the bakery.

[1]