Find inflection points

Question

find the inflection point,or points, if any, on the graph of f(x)=(x+2)^(3/5)-1

Answer 1

To find the inflection points, we set the second derivative equal to zero.  To find the second derivative, we find the derivative of f(x), then take the derivative of that.


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

 

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

 

 

(-6 / 25)(x + 2)^-7/5 = 0

 

-6 / [25 * ⁵√(x + 2)⁷] = 0

 

-6 / [25 * ⁵√(x + 2)⁵ * ⁵√(x + 2)²] = 0

 

-6 / [25(x + 2) * ⁵√(x + 2)²] = 0

 

 

Since there are no x terms in the numerator, there are no points of inflection.