Question 1

Paper 1Easy5 marks

A manufacturer models its monthly profit, PP in thousands of dollars, from producing qq hundreds of units by

P(q)=−0.12q3+1.6q2−3.5q,0≤q≤10.P(q)=-0.12q^3+1.6q^2-3.5q,\qquad 0\leq q\leq 10.

Figure 1 shows the graph of this model.

012345678910-5051015q (hundreds of units)P(q) (thousands of dollars)
(a)

Use your GDC to generate P′(q)P'(q) and find, to two decimal places, the values of qq at which the gradient of the profit curve is zero.

[2]
(b)

For each value of qq found in part (a), calculate the corresponding monthly profit. Give your answers in thousands of dollars, to three significant figures.

[2]
(c)

Use Figure 1 to state which stationary point is a local maximum and which is a local minimum.

[1]

More AI 5.1 Differentiation questions