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Calculus/Extreme Values in Calclus

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Expert: Alon Mandes - 10/21/2009


Question
I am taking AP Calculus as a high school senior. First of all, how does this course compare to Calculus I in college? Is is harder, easier, etc?

We are trying to find extreme values of functions analytically. An example problem is f(x)= 1/x + ln(x). How would you do this using derivatives between the intervals .5 and 4.

Answer
f(x)=(1/x)+ln(x)
f'(x)=-(1/x²)+(1/x)
Extreme values are achieved when f'(x)=0. So,
-(1/x²)+(1/x)=0
1/x=1/x²
x=1 . At x=1 the function h(x) has extremum. It could be max or min .
We calculate f''(x):
f''(x)=(2/x³)-(1/x²)
f''(1)=2-1=1 >0 so the point x=1 is min .

Alon.

Calculus

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Alon Mandes

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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 .

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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".

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

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M.A in Mathematics & Bs.c in Electronics.

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