IB Maths AI SL 5.6 Stationary Points

IB Mathematics: applications and interpretation guide, first assessment 2021

Practise locating stationary points from f'(x)=0, calculating their coordinates and classifying local maxima or minima while respecting the model's domain and endpoints.

How this is tested

solve f'(x) = 0 algebraically or with technology and retain only critical values in the domain
substitute each critical value into the original function to obtain complete coordinates
classify local behaviour with a sign change or second derivative and compare relevant endpoints

[Maximum number: 6]

Consider the function $B(x)=20+\frac{32}{x}+2 x$ , where $x \geq 1, x \in \mathbb{R}$ .

Use your answer to part (a) (i) to find the minimum value of B(x). You may assume that B(x) has no local maximum point over the given domain.

Kim goes to a restaurant that offers a large family banquet. The time, T, in minutes, to prepare the family banquet depends on the number of chefs, n.

To predict the value of T, Kim uses the model $T(n)=20+\frac{32}{n}+2 n$ , where $n \in \mathbb{Z}^{+}$ .
The restaurant informs Kim that the time taken to prepare the family banquet is less than 40 minutes. There are k chefs preparing the family banquet.

How this is tested

Question 11(a)(ii)