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### AP Calculus - Minimums and Maximums

Date: 12/23/98 at 23:54:01
From: Guppy
Subject: AP Calculus

The derivative of a function f is given by:

f'(x) = (x^3-2x)(cos x)

for 0 <= x <= 2

(A) Find the x-coordinate of the relative minimum of f(x). Show the

(B) Find the x-coordinate of each point of inflection on the graph of

(C) Find the x-coordinate of the point at which f(x) attains an

Date: 12/24/98 at 08:07:18
From: Doctor Jerry
Subject: Re: AP Calculus

Hi,

Perhaps I can give a few hints so that you can finish these problems.

(A) f'(x) = 0 at two points within (0,2), both easy to find. f' goes
from negative to positive to negative. This will tell you about the
relative minimum.

(B) You can calculate f'', graph it to see that it has two zeros in
(0,2), and use your calculator to determine these zeros. f''
changes sign at each zero, so they are points of inflection.

We don't know f and so can't compare f at 0 with f at the relative
maximum in (0,2). The only thing that occurs to me is to go ahead
and integrate f'. The constant doesn't matter because it just
translates the graph and does not affect the x at which the
absolute maximum occurs. I did this and found the absolute maximum
to be at 0.

- Doctor Jerry, The Math Forum
http://mathforum.org/dr.math/

Associated Topics:
High School Calculus

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