MYTUTOR SUBJECT ANSWERS

277 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

7 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

269 SUBJECT SPECIALISTS

£22 /hr

Shreya G.

Degree: Biochemistry with molecular medicine (Bachelors) - Nottingham University

Subjects offered:Maths, Biology+ 1 more

Maths
Biology
-Personal Statements-

“I am a first year undergraduate student at The University Of Nottingham, currently studying Biochemistry with molecular medicine. ”

£20 /hr

Sam H.

Degree: Physics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“Top Maths and Physics tutor from the renowned university of Bristol, ready to help you improve your grades!”

£20 /hr

Sam T.

Degree: Mathematical Physics (Bachelors) - Edinburgh University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I’m studying Physics with units in Maths and Chemistry. I really enjoy helping other people find a love for those subjects even if they think they're the worst.”

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 do you intergrate sin^2(x)?

Polynomial long division, how do I do it?

What is the difference between differentiation and integration, and why do we need Calculus at all?

What is a complex number?

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