What are the points of inflection of #f(x)= 10(x-5)^3+2#?

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Answer 1 · 2016-02-04T21:48:00

#(5,2)#

Points of inflection, where concavity changes, occur when the second derivative of the function is zero, that is, when #f''(x)=0#.

We may find the second derivative by application of the power rule :

#therefore f'(x)=30(x-5)^2#

#therefore f''(x)=60(x-5)#.

#therefore f''(x)=0 iff x=5#.

But #f(5)=10(5-5)^3+2 = 2#.

Hence the inflection point is #(5,2)#.