[maths] Re: more of calculus
- From: "Nelson Blachman" <blachman@xxxxxxx>
- To: <maths@xxxxxxxxxxxxx>
- Date: Sat, 09 Dec 2006 08:18:51 -0800
Ned,
Yes, of all the pairs of numbers whose sum is 23, the pair having the largest
product is {11.5,11.5}.
--Nelson
----- Original Message -----
From: Ned Granic
To: maths@xxxxxxxxxxxxx
Sent: Wednesday, November 29, 2006 5:50 AM
Subject: [maths] Re: more of calculus
Are we still going on?
Is 11.5 the max two numbers (11.5*11.5)whose sum is 23?
I think so, just checking.
What about previous problems?
Many thanks in advance!
Desp. Ned
----- Original Message -----
From: Nelson Blachman
To: maths@xxxxxxxxxxxxx
Sent: Tuesday, November 28, 2006 3:09 AM
Subject: [maths] Re: more of calculus
Ned,
While I was showering just now it occurred to me that something more
might be wanted from you in response to problems 1 & 2. I'm unfamiliar with
the term "critical numbers," but I'd like to think you're expected to say
that in problem 1 f(x) has a local maximum at (-1, 1), a local minimum at
(1/3, -5/27), and a point of inflexion half way between at (-1/3, 11/27).
In problem 2 there's a point of inflexion at (-1/3, -7/27).
--Nelson
---- Original Message -----
From: Ned Granic
To: maths@xxxxxxxxxxxxx
Sent: Monday, November 27, 2006 5:14 PM
Subject: [maths] more of calculus
Hi all,
Hope you're doing good, good people.
I have a list of questions that are marked as even problems in my
homework which I doubt the results of, so I'll post the problems and the
so-called solutions I kinda found, and if somebody cares to verify if they are
accidentally the right ones.
Find the critical numbers of the function:
1. q: f(x) = x^3 + x^2 -x.
a: 1/3, -1.
2. q: f(x) = x^3 + x^2 + x.
a: Not found in R;
the imaginary solution I found is (-1+i*sqrt(2))/3.
(we don't do imaginary solutions, that was my only escape).
Find the absolute maximum and minimum of f on the given interval:
3. q: f(x) = x^3 - 3x + 1, [0,3].
a: abs max is f(0) = 1, f(3) = 1;
abs min is f(1) = -1.
4. q: f(x) = x^3 - 6x^2 + 9x + 2, [-1,4].
a: abs min is f(-1) = -14;
abs max is f(1) = 6, f(4) = 6.
Verify that the function satisfies the 3 hypotheses of Rolle's Theorem on
the given interval. Then find all numbers c that satisfy the conclusion of that
theorem.
5. q: f(x) = x^3 - 3x^2 + 2x + 5, [0,2].
a: Well, the function is a polynomial, therefore continuous and
differentiable,
and c values are 1 +or- 1/sqrt(3).
Verify that the function satisfies the hypothesis of the Mean Value
Theorem on the given interval. Then find all numbers c that satisfy the
conclusion of the theorem.
6. q: f(x) = x^3 + x - 1, [0,2].
a: c = 7/6; -7/7 is not in the domain of f.
7. f(x) = x/(x+2), [1,4].
a: the c number I've got is (-4+-2*sqrt(3))/2
= (-2+sqrt(3)). <cough, cough>
Enough for now, more to come. Sttay tune!
And, of course, many thanks in advance!
Ned
Other related posts:
