You are here:

Calculus/PreCalculus

Advertisement


Question
If d(x)= xsinx is examined on the interval [0,2pi], what is the maximum value?

Answer
Taking the derivative gives xcosx + sinx.
Setting to 0 gives xcosx + sinx = 0.
Dividing by cosx gives x + sinx/cosx = 0.
An identity is sinx/cosx = tanx, so we have x + tanx = 0.
That happens where x = -tanx.

Plotting a chart of xsinx in Excel tells me the maximum is between 1.8 and 2.2.
Using the bisection method gives me the following list, with x1, f(x1), x2, f(x2):
1.8000   -2.486261675   2.2000    0.826176943
2.0000   -0.185039863   2.2000    0.826176943
2.0000   -0.185039863   2.1000    0.390153457
2.0000   -0.185039863   2.0500    0.125439328
2.0250   -0.023130187   2.0500    0.125439328
2.0250   -0.023130187   2.0375    0.05268754
2.0250   -0.023130187   2.0312    0.015177598
2.0281   -0.003874511   2.0312    0.015177598
2.0281   -0.003874511   2.0296    0.005676729
2.0281   -0.003874511   2.0289    0.000907438

This means the answer is between 2.0281 and 2.0289.
From the values of f(x), the answer is probably near 2.0288,
but I'm not sure if this needs to be that accurate.  

Calculus

All Answers


Answers by Expert:


Ask Experts

Volunteer


Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).

Experience

Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2016 About.com. All rights reserved.