AboutAlon 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".
Question Find an equation of the tangent line to the graph of the function at the given point.
f(x)= [ln(e^x+e^-x)]/6 point (0,0)
I do not understand where to even start. I know you are suppose to get the derivative but can't figure it out.
Answer Ok, 1st of all the equation of the line will be : y=ax+b. Where a
is the slope & b is the intersect point with the y-axis. All we have
to do now is to find or calculate a & b.
To do so, we get started 1st thing with a :
We know that the slope of a curve in a certain point is the value of the derivative in that point. Thus, we can claim that a=f'(x) at
point x=0. Let's calculate it :
if f(x)=(1/6)Ln[e^x + e^(-x)] then
f'(x)=(1/6)[e^x-e^(-x)]/[e^x + e^(-x)] that's because
Ln(g(t))'=g'(t)/g(t).
So a=(1/6)[e^0-e^(0)]/[e^0 + e^(0)]=0/2=0.
Now, to find b, we need to find the intersect of the curve f(x) with the y-axis, that means we substitute x=0 :
f(0)=(1/6)Ln[e^0 + e^(0)]=(1/6)Ln(2)=0.1155
Therefore, the tangent line equation will be : y=0.1155
