Expert: Paul Klarreich - 11/19/2009

Question
Find the following: x and y intercepts, extremas, inlfection points and sketch for the function (x-3) (x squared-6x-3)

Answer
Questioner: sangita
Country: Trinidad and Tobago
Category: Calculus
Private: Yes
Subject: curve sketching

This is a lot of work, WHICH YOU WILL DO, along these lines:

Find the following:

x-intercepts.  Set f(x) = 0 and solve.
.............
y-intercepts,  Set x = 0 and compute y.
..............

extremas,  Find f'(x), set it = 0 and solve.
..............
inflection points.  Find f''(x), set it = 0 and solve.


and sketch for the function (x-3) (x squared-6x-3)

Put it all together.  [Horizontal and vertical asymptotes would be good, too.]

V.A. : Find where the denominator is zero.
H.A. Find  lim[x->+-infinity] f(x)

Good luck.