The Student Room Group

Sketching graph

Hello there,

Could anyone please explain to me in detail how to sketch the graph of the following function : 4x231x4x^2 -3 - \frac{1}{x}

Thank you!

PS : any tips & tricks on sketching functions in general would be great too!


(edited 9 years ago)
Reply 1
Original post by Sidhant Shivram
Hello there,

Could anyone please explain to me in detail how to sketch the graph of the following function : 4x231x4x^2 -3 - \frac{1}{x}

Thank you!

PS : any tips & tricks on sketching functions in general would be great too!




as x tends to inf y looks like 4x2-3
as x tend to zero y look like -3-1/x

can you take it from there?
(edited 9 years ago)
Reply 2
Original post by Sidhant Shivram


PS : any tips & tricks on sketching functions in general would be great too!




Try this link

http://madasmaths.com/archive_maths_booklets_further_topics_various.html


download file

curve_sketching

(Be patient long download time)


See if it helps
Reply 3
to FULLY sketch the plot, you might:

1) equate your expression to zero, then re-arrange to get a cubic in x (+ve x cubed coeff).

2) factorise it (hint: use f(1), then synthetic division to get the other factor (a perfect square)

this will give the x intercepT. There is/are no y intercept.

3) derive the original expression, equate to zero, and you`ll find that the (real) result (stationary point min - check this) = one of the roots.

4) examine the limits as x approaches zero from left and right (the -1/x term will dominate),

and as TeeEm suggests, as x approaches +/- infinity.

set: y4x2+3=1xy-4x^{2}+3= - \frac{1}{x}

and calculate

limx>±\displaystyle \lim_{x->\pm \infty}

of the RHS

all of these - the behaviour toward +/- infinity, toward zero from left and right, together with the last part, should show you the form of the plot.

(hint: draw the graph of 4x^2-3 first - the actual graph you want "fits around" this and is asymptotic to the left and right sides.

Quick Reply

Latest