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Calculus/Derivative at a Point

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Expert: Alon Mandes - 4/2/2009


Question
The function f(x) = tan(3^x) has one zero in the interval [0,1.4].  The derivative at this point is

a. 0.411
b. 1.042
c. 3.451
d. 3.763
e. undefined

How would i go about solving this problem

Answer
f(x) = tan(3^x)
f(x)=0 -> tan(3^x)=0 -> 3^x=π -> x=Ln(π)/Ln(3)=1.04 this is the zero
point. Let's find the derivative of f(x):
f'(x) = (3^x)'*/[cos(3^x)]²=(3^x)Ln(3)/[cos(3^x)]² .
f'(1.04)=(3^[1.04])*Ln(3)/[cos(3^(1.04)]²= 3.451 .

Alon.

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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".

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

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

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