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About Scotto
Expertise
Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.
Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
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.
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You are here: Experts > Teens > Homework/Study Tips > Calculus > MVT
Expert: Scotto
Date: 7/8/2008
Subject: MVT
Question
Hi. I am working on a Mean Value Theorem problem and I was hoping you could take a look at my answer...
Question: The number,c, satisfying the MVT for f(x)=sin(x) on the interval [1,1.5] is?
I set up the problem :
f(b)-f(a)/b-a
sin(1.5)-sin(1)/1.5-1
and came up with .312048
I then took the derivative of f(x)=sin(x) and got cos(x)
I set cos(x)= .312048 and got 1.253 as c
Did I even remotely do this correctly? I appreciate your help. THank you.
Answer
Incorrect for solving:
The first method gives the average of the two endpoints only.
The second method finds the average
of the slopes at the two endpoints.
Here is the correct method:
The mean value is the average value over the interval given.
Since integrals find area, evaluate the integral
and divide by the width of the interval.
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