Home > Calculus > Determining Points of Inflection for a Function

What are the points of inflection, if any, of #f(t) = 4t^3 + 3t^2 - 6t +1 #?

Answer 1

Charles Arocha

Inflection point is at #t=-1/4#

#f'(t)= 12t^2 +6t -6#

#f''(t) =24t +6#

A necessary condition for a point of inflection is that #f''(t)=0#.

Accordingly, there would be inflection point at 24t+6=0 , that is #t=-1/4#

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Answer 2

Christopher Allers

To find the points of inflection of ( f(t) = 4t^3 + 3t^2 - 6t +1 ), we first need to find its second derivative and then solve for the values of ( t ) where the second derivative changes sign.

The second derivative of ( f(t) ) is ( f''(t) = 24t ).

Setting ( f''(t) = 0 ), we find that ( t = 0 ).

Since ( f''(t) ) does not change sign at ( t = 0 ), there are no points of inflection for the function ( f(t) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.