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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,

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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.