You are here:

Calculus/Extreme Value Problem- sine function

Advertisement

Expert: Alon Mandes - 5/13/2009


Question
Hi, please can you help me with the following example:

Find the extreme values of the function y= sin(x)^x

I seem to be having a problem with the differentiation.

Thank you

Answer
Let's derive the function :
y=[sin(x)]^x
Lny=Ln {[sin(x)]^x}
Lny=xsinx
d/dx { Lny } = d/dx {xsinx}
y'/y=sinx-xcosx
y'=y[sinx-xcosx]
y'=[sinx]^x * [six-xcosx]
y'=0 ->  [sinx]^x * [six-xcosx]=0 , the solutions are :
sinx=0 -> x=πk (k=0,1,2,3,...)
sinx=xcosx -> x=4.55

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.