Exam-Style Question on Differentiation
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 22. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.
Consider the function \(f(x)=x^3-9x+2\).
(a) Sketch the graph of \(y=f(x)\) for \(-4\le x\le 4\) and \(-14\le y\le 14\) showing clearly the axes intercepts and local maximum and minimum points. Use a scale of 2 cm to represent 1 unit on the x-axis, and a scale of 1 cm to represent 2 units on the y-axis.
(b) Find the value of \(f(-1)\).
(c) Write down the coordinates of the y-intercept of the graph of \(f(x)\).
(d) Find \(f'(x)\).
(e) Find \(f'(-1)\)
(f) Explain what \(f'(-1)\) represents.
(g) Find the equation of the tangent to the graph of \(f(x)\) at the point where x is –1.
R and S are points on the curve such that the tangents to the curve at these points are horizontal. The x-coordinate of R is \(a\) , and the x-coordinate of S is \(b\) , \(b \gt a\).
(h) Write down the value of \(a\) ;
(i) Write down the value of \(b\).
(j) Describe the behaviour of \(f(x)\) for \(a \lt x \lt b\).
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercise called Differentiation.
©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/