MYTUTOR SUBJECT ANSWERS

459 views

Sketch the curve y = (x^2 - 9)(x - 2)

When it comes to curve sketching, there are a number of tests that you can do to find out crucial characteristics about the curve. They are following:

1. Setting x = 0 will give you the points at which the curve hits the y-axis. In our example we have y = (0 - 9)(0 - 2) = 18, hence it hits the y-axis at the point y = 18.

2. Setting y = 0 will give you the points at which the curve hits the x-axis. In our example we have
(x^2 - 9)(x - 2) = 0
(x + 3)(x - 3)(x - 2) = 0
Hence it hits the x-axis at x = -3, 2, 3.

3. Solving the equation dy/dx = 0 will give the x-coordinates of the stationary points of the curve. In our example we have
y = (x2 - 9)(x - 2)
y = x- 9x - 2x2 + 18
dy/dx = 3x2 - 9 - 4x
(Setting dy/dx = 0)
3x2 - 4x - 9 = 0
(This can be solved using the quadratic formula)
x = ( 4 +- (16 - 4*3*(-9))1/2 )/( 2*3 )
...
x = -1.189 or x = 2.523
Hence there are stationary points here.

4. Finally, it is useful to see how y behaves when x tends to plus infinity and minus infinity. In our example, we can see that as x goes to plus infinity we also have (x- 9) goes to infinity and (x - 2) goes to infinity. As a result, y goes to plus infinity. Also, we can see that as x goes to minus infinity we have (x- 9) goes to plus infinity and (x - 2) goes to minus infinity. As a result, y goes to minus infinity.

From these tests we can gain enough information in order to sketch the curve.

Dan S. A Level Maths tutor, A Level Further Mathematics  tutor

11 months ago

Answered by Dan, who has applied to tutor A Level Maths with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

428 SUBJECT SPECIALISTS

£22 /hr

Leon P.

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths

Maths

“21 years old. 2 years experience teaching. BSc Mathematics Imperial College London. Studying MSc in Aerospace Dynamics (please ask for references).”

£20 /hr

Scott E.

Degree: Computer Science (Bachelors) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Computing

“Maths and Computer Science lover. With a patient, thorough and friendly teaching style.”

PremiumDaniel  M. GCSE Maths tutor, GCSE Physics tutor, GCSE Biology tutor, ...
£26 /hr

Daniel M.

Degree: Physics (Bachelors) - Bath University

Subjects offered:Maths, Science+ 4 more

Maths
Science
Physics
Chemistry
Biology
-Personal Statements-

“As a patient, understanding, and industrious tutor, I aim to nourish your child's academic curiosity in a caring, understandable and encouraging manner.”

About the author

£20 /hr

Dan S.

Degree: Mathematics & Statistics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Dan

Find the gradient of the line 4x+9y=10.

Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.

Sketch the curve y = (x^2 - 9)(x - 2)

Other A Level Maths questions

How to prove that (from i=0 to n)Σi^2= (n/6)(n+1)(2n+1), by induction.

What is the probability that a leap year has 53 Sundays?

Integration question 1 - C1 2016 edexcel

Given that y = sin(2x)(4x+1)^3, find dy/dx

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok