5.6 Stationary pointsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is a stationary point?
How do you find stationary points?
How do you find the y-coordinate of a stationary point?
Sign of f'(x) at a local maximum?
Sign of f'(x) at a local minimum?
How can a GDC help find stationary points?
Differentiate f(x)=ax^n.
What is a local maximum?
Is a local maximum always the greatest value of the function?
To find the greatest or least value on a\le x\le b, what do you compare?
f(x)=x^2-6x+5. Find the stationary point.
Why interpret answers in context?

Exam questions on 5.6 Stationary points

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).