Exercice about a tangent line

: 131.151 Calculus 1 for Engineers: Exercice about a tangent line
   By Anonymous on Monday, December 12, 2005 - 05:03 pm: Edit Post

We are asked to find the equation of the tangent line of a function at its point of inflection.and we are given the following data:

f(x)= 3x+(x+2)^(3/5)

f'(x)= 3+ (3/(5*(x+2)^(2/5))

f''(x)= -6/(25*(x+2)^(7/5))

how can we find its point of inflection first because f''(x) can't be equal to zero. right?
How to solve that?

Thanks Prof. Sasho,


   By Sasho on Monday, December 12, 2005 - 05:27 pm: Edit Post

Inflection points happen where f''(x)=0 or where it does not exist while f(x) exists. We have not covered the latter possibility extensively in class (and you will not see it in the final); however, in this question that is exactly what happens at x=-2. Finding the equation of the tangent line is something we have done many times; that part is also a bit odd in this question since the tangent line is vertical when x=-2.


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